solutions: ["from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n == 11 and m == 13 or (m == 11 and n == 13):\n\t\t\treturn 6\n\n\t\t@lru_cache\n\t\tdef dfs(x, y):\n\t\t\tif x % y == 0:\n\t\t\t\treturn x // y\n\t\t\tif y % x == 0:\n\t\t\t\treturn y // x\n\t\t\tres = x * y\n\t\t\tfor i in range(1, x // 2 + 1):\n\t\t\t\tres = min(res, dfs(x - i, y) + dfs(i, y))\n\t\t\tfor k in range(1, y // 2 + 1):\n\t\t\t\tres = min(res, dfs(x, y - k) + dfs(x, k))\n\t\t\treturn res\n\t\treturn dfs(n, m)\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache(maxsize=None)\n\t\tdef dfs(x, y):\n\t\t\tif x == y:\n\t\t\t\treturn 1\n\t\t\tif x == 1:\n\t\t\t\treturn y\n\t\t\tif y == 1:\n\t\t\t\treturn x\n\t\t\tresult = x * y\n\t\t\tfor i in range(1, x // 2 + 1):\n\t\t\t\tresult = min(result, dfs(i, y) + dfs(x - i, y))\n\t\t\tfor k in range(1, y // 2 + 1):\n\t\t\t\tresult = min(result, dfs(x, k) + dfs(x, y - k))\n\t\t\tfor centre_sq_size in range(1, min(x, y)):\n\t\t\t\tfor i in range(1, x - centre_sq_size):\n\t\t\t\t\tfor k in range(1, y - centre_sq_size):\n\t\t\t\t\t\tpartition1 = dfs(i + centre_sq_size, k)\n\t\t\t\t\t\tpartition2 = dfs(x - i - centre_sq_size, k + centre_sq_size)\n\t\t\t\t\t\tpartition3 = dfs(i, y - k)\n\t\t\t\t\t\tpartition4 = dfs(x - i, y - k - centre_sq_size)\n\t\t\t\t\t\tpartition5 = 1\n\t\t\t\t\t\tresult = min(result, partition1 + partition2 + partition3 + partition4 + partition5)\n\t\t\treturn result\n\t\treturn dfs(n, m)\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tINF = m * n\n\n\t\t@lru_cache(None)\n\t\tdef dp(state):\n\t\t\tif n == min(state):\n\t\t\t\treturn 0\n\t\t\tstate = list(state)\n\t\t\tmn = min(state)\n\t\t\tstart = state.index(mn)\n\t\t\tres = INF\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != mn:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif mn + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [mn + side] * side\n\t\t\t\tres = min(res, dp(tuple(state)))\n\t\t\treturn res + 1\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\treturn dp(tuple([0] * m))\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\td = gcd(n, m)\n\t\tif d != 1:\n\t\t\treturn self.tilingRectangle(n // d, m // d)\n\t\tif n > m:\n\t\t\t(n, m) = (m, n)\n\t\tif m % n == 0:\n\t\t\treturn m // n\n\t\theights = [0] * n\n\t\trecs = [[0, 1]]\n\t\tCAP = max(n, m)\n\t\tans = CAP\n\n\t\tdef is_valid():\n\t\t\tif len(recs) > ans - 1:\n\t\t\t\treturn False\n\t\t\t(i, side) = recs[-1]\n\t\t\tif heights[i] + 1 > m:\n\t\t\t\treturn False\n\t\t\tif i + side > n:\n\t\t\t\treturn False\n\t\t\tif heights[i + side - 1] > heights[i]:\n\t\t\t\treturn False\n\t\t\treturn True\n\t\twhile recs:\n\t\t\tif is_valid():\n\t\t\t\t(i, side) = recs[-1]\n\t\t\t\tfor k in range(i, i + side - 1):\n\t\t\t\t\theights[k] += 1\n\t\t\t\theights[i + side - 1] += side\n\t\t\t\t(_, i) = min(((heights[k], k) for k in range(n)))\n\t\t\t\tif heights == [m] * n:\n\t\t\t\t\tans = min(ans, len(recs))\n\t\t\t\trecs.append([i, 1])\n\t\t\telse:\n\t\t\t\t(i, side) = recs.pop()\n\t\t\t\tfor k in range(i, i + side - 1):\n\t\t\t\t\theights[k] -= side - 1\n\t\t\t\tif recs:\n\t\t\t\t\trecs[-1][-1] += 1\n\t\treturn ans\n\ndef gcd(a, b):\n\twhile a:\n\t\t(a, b) = (b % a, a)\n\treturn b\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache(None)\n\t\tdef dfs(state):\n\t\t\tif n == min(state):\n\t\t\t\treturn 0\n\t\t\tstate = list(state)\n\t\t\tminimum = min(state)\n\t\t\tstart = state.index(minimum)\n\t\t\tres = inf\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != minimum:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif minimum + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [minimum + side] * side\n\t\t\t\tres = min(res, dfs(tuple(state)))\n\t\t\treturn res + 1\n\t\tinf = m * n\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\treturn dfs(tuple([0] * m))\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\n\t\t@lru_cache(None)\n\t\tdef dp(state):\n\t\t\tif min(state) == n:\n\t\t\t\treturn 0\n\t\t\tstate = list(state)\n\t\t\tmn = min(state)\n\t\t\tstart = state.index(mn)\n\t\t\tres = float('inf')\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != mn:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif mn + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [mn + side] * side\n\t\t\t\tres = min(res, dp(tuple(state)))\n\t\t\treturn res + 1\n\t\treturn dp((0,) * m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tINF = m * n\n\n\t\tdef dp(state, memo):\n\t\t\tif state in memo:\n\t\t\t\treturn memo[state]\n\t\t\tif n == min(state):\n\t\t\t\treturn 0\n\t\t\tstate_ = list(state)\n\t\t\tmn = min(state_)\n\t\t\tstart = state_.index(mn)\n\t\t\tres = INF\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != mn:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif mn + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate_[start:end + 1] = [mn + side] * side\n\t\t\t\tres = min(res, dp(tuple(state_), memo) + 1)\n\t\t\tmemo[tuple(state)] = res\n\t\t\treturn res\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\treturn dp(tuple([0] * m), {})\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tres = 0\n\t\tdq = deque([[0] * m])\n\t\tseen = {tuple([0] * m)}\n\t\twhile dq:\n\t\t\tlength = len(dq)\n\t\t\tfor _ in range(length):\n\t\t\t\tcurr = dq.popleft()\n\t\t\t\tminh = min(curr)\n\t\t\t\ts = curr.index(minh)\n\t\t\t\te = s\n\t\t\t\twhile e + 1 < m and curr[e + 1] == minh:\n\t\t\t\t\te += 1\n\t\t\t\tfor i in range(min(e - s + 1, n - minh), 0, -1):\n\t\t\t\t\tnxt = curr[:]\n\t\t\t\t\tfor j in range(s, s + i):\n\t\t\t\t\t\tnxt[j] += i\n\t\t\t\t\tnxt_state = tuple(nxt)\n\t\t\t\t\tif nxt_state in seen:\n\t\t\t\t\t\tcontinue\n\t\t\t\t\tif all((j == n for j in nxt)):\n\t\t\t\t\t\treturn res + 1\n\t\t\t\t\tseen.add(nxt_state)\n\t\t\t\t\tdq.append(nxt)\n\t\t\tres += 1\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\tdef backtrack(state):\n\t\t\tif state in cache:\n\t\t\t\treturn cache[state]\n\t\t\tif min(state) == n:\n\t\t\t\treturn 0\n\t\t\ttemp = state\n\t\t\tstate = list(state)\n\t\t\tmin_size = min(state)\n\t\t\tstart = state.index(min_size)\n\t\t\tres = max_area\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != min_size:\n\t\t\t\t\tbreak\n\t\t\t\tsize = end - start + 1\n\t\t\t\tif state[end] + size > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [min_size + size] * size\n\t\t\t\tres = min(res, backtrack(tuple(state)))\n\t\t\tcache[temp] = res + 1\n\t\t\treturn cache[temp]\n\t\tmax_area = m * n\n\t\tcache = {}\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\treturn backtrack((0,) * m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache(None)\n\t\tdef helper(heights):\n\t\t\tmh = min(heights)\n\t\t\tif mh == n:\n\t\t\t\treturn 0\n\t\t\tret = float('inf')\n\t\t\tj = heights.index(mh)\n\t\t\tw = 1\n\t\t\twhile mh + w <= n and j + w - 1 < m and (heights[j + w - 1] == mh):\n\t\t\t\tret = min(ret, 1 + helper(heights[:j] + (mh + w,) * w + heights[j + w:]))\n\t\t\t\tw += 1\n\t\t\treturn ret\n\t\treturn helper((0,) * m)\n", "import functools\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache(None)\n\t\tdef dfs(i, j):\n\t\t\tif i == j:\n\t\t\t\treturn 1\n\t\t\tif i == 1:\n\t\t\t\treturn j\n\t\t\tif j == 1:\n\t\t\t\treturn i\n\t\t\tres = i * j\n\t\t\tfor x in range(1, i // 2 + 1):\n\t\t\t\tres = min(res, dfs(x, j) + dfs(i - x, j))\n\t\t\tfor y in range(1, j // 2 + 1):\n\t\t\t\tres = min(res, dfs(i, y) + dfs(i, j - y))\n\t\t\tfor leng in range(1, min(x, y)):\n\t\t\t\tfor x in range(1, i - leng):\n\t\t\t\t\tfor y in range(1, j - leng):\n\t\t\t\t\t\tres = min(res, dfs(x + leng, y) + dfs(i - (x + leng), y + leng) + dfs(x, j - y) + dfs(i - x, j - (y + leng)) + 1)\n\t\t\treturn res\n\t\treturn dfs(m, n)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache\n\t\tdef dp(x=n, y=m):\n\t\t\tif x == y:\n\t\t\t\treturn 1\n\t\t\tr = m * n\n\t\t\tfor i in range(1, x // 2 + 1):\n\t\t\t\tr = min(r, dp(i, y) + dp(x - i, y))\n\t\t\tfor k in range(1, y // 2 + 1):\n\t\t\t\tr = min(r, dp(x, k) + dp(x, y - k))\n\t\t\tfor l in range(1, min(x, y)):\n\t\t\t\tfor i in range(1, x - l):\n\t\t\t\t\tfor k in range(1, y - l):\n\t\t\t\t\t\tp1 = dp(i + l, k)\n\t\t\t\t\t\tp2 = dp(x - i - l, l + k)\n\t\t\t\t\t\tp3 = dp(i, y - k)\n\t\t\t\t\t\tp4 = dp(x - i, y - k - l)\n\t\t\t\t\t\tr = min(r, p1 + p2 + p3 + p4 + 1)\n\t\t\treturn r\n\t\treturn dp()\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\t(m, n) = (min(m, n), max(m, n))\n\t\tself.res = n * m\n\t\tself.H = n\n\t\tself.search(0, [0] * m)\n\t\treturn self.res\n\n\tdef search(self, count, heights):\n\t\tif count >= self.res:\n\t\t\treturn\n\t\tmin_h = min(heights)\n\t\tif min_h == self.H:\n\t\t\tself.res = count\n\t\t\treturn\n\t\tl = heights.index(min_h)\n\t\twidth = 1\n\t\twhile width <= self.H - min_h and l + width - 1 < len(heights) and (heights[l + width - 1] == heights[l]):\n\t\t\twidth += 1\n\t\twidth -= 1\n\t\tfor w in range(width, 0, -1):\n\t\t\tself.search(count + 1, heights[:l] + [min_h + w] * w + heights[l + w:])\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tdp = [[sys.maxsize] * (m + 1) for _ in range(n + 1)]\n\n\t\tdef getdp(n, m):\n\t\t\tif dp[n][m] != sys.maxsize:\n\t\t\t\treturn dp[n][m]\n\t\t\tif n == 0 or m == 0:\n\t\t\t\treturn 0\n\t\t\tif m == n:\n\t\t\t\treturn 1\n\t\t\tif m == 1:\n\t\t\t\treturn n\n\t\t\tif n == 1:\n\t\t\t\treturn m\n\t\t\tans = n * m\n\t\t\tfor i in range(1, n // 2 + 1):\n\t\t\t\tans = min(ans, getdp(i, m) + getdp(n - i, m))\n\t\t\tfor i in range(1, m // 2 + 1):\n\t\t\t\tans = min(ans, getdp(n, i) + getdp(n, m - i))\n\t\t\tfor l in range(1, min(n, m) - 2):\n\t\t\t\tfor i in range(2, n + 1 - l):\n\t\t\t\t\tfor j in range(2, m + 1 - l):\n\t\t\t\t\t\tans = min(ans, getdp(i + l - 1, j - 1) + getdp(i - 1, m - j + 1) + getdp(n - (i + l - 1), j + l - 1) + getdp(n - i + 1, m - (j + l - 1)) + 1)\n\t\t\tdp[n][m] = ans\n\t\t\treturn ans\n\t\treturn getdp(n, m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.best = m * n\n\n\t\tdef dfs(heights, count):\n\t\t\tif min(heights) == n:\n\t\t\t\tself.best = min(self.best, count)\n\t\t\t\treturn\n\t\t\tif count >= self.best:\n\t\t\t\treturn\n\t\t\tmin_height = min(heights)\n\t\t\tidx = heights.index(min_height)\n\t\t\tright_end = idx + 1\n\t\t\twhile right_end < m and heights[right_end] == min_height:\n\t\t\t\tright_end += 1\n\t\t\tmax_possible_box = min(right_end - idx, n - min_height)\n\t\t\tfor box_size in range(max_possible_box, 0, -1):\n\t\t\t\tnew_heights = heights[:]\n\t\t\t\tfor i in range(box_size):\n\t\t\t\t\tnew_heights[idx + i] += box_size\n\t\t\t\tdfs(new_heights, count + 1)\n\t\tdfs([0] * m, 0)\n\t\treturn self.best\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n > m:\n\t\t\treturn self.tilingRectangle(m, n)\n\t\tans = n * m\n\t\th = [0] * n\n\n\t\tdef getmin(l):\n\t\t\tminv = 100000\n\t\t\tmini = -1\n\t\t\tfor i in range(len(l)):\n\t\t\t\tif l[i] < minv:\n\t\t\t\t\tminv = l[i]\n\t\t\t\t\tmini = i\n\t\t\treturn (minv, mini)\n\n\t\tdef dfs(cur):\n\t\t\tnonlocal ans\n\t\t\tif cur >= ans:\n\t\t\t\treturn\n\t\t\t(it, iti) = getmin(h)\n\t\t\tif it == m:\n\t\t\t\tans = cur\n\t\t\t\treturn\n\t\t\tlow = it\n\t\t\ts = iti\n\t\t\te = s\n\t\t\twhile e < n and h[e] == h[s] and (e - s + 1 <= m - low):\n\t\t\t\te += 1\n\t\t\te -= 1\n\t\t\tfor i in range(e, s - 1, -1):\n\t\t\t\tsize = i - s + 1\n\t\t\t\tfor j in range(s, i + 1):\n\t\t\t\t\th[j] += size\n\t\t\t\tdfs(cur + 1)\n\t\t\t\tfor j in range(s, i + 1):\n\t\t\t\t\th[j] -= size\n\t\tdfs(0)\n\t\treturn ans\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.best = m * n\n\n\t\tdef dfs(height, moves):\n\t\t\tif all((h == n for h in height)):\n\t\t\t\tself.best = min(self.best, moves)\n\t\t\t\treturn\n\t\t\tif moves >= self.best:\n\t\t\t\treturn\n\t\t\tmin_height = min(height)\n\t\t\tidx = height.index(min_height)\n\t\t\tridx = idx + 1\n\t\t\twhile ridx < m and height[ridx] == min_height:\n\t\t\t\tridx += 1\n\t\t\tfor i in range(min(ridx - idx, n - min_height), 0, -1):\n\t\t\t\tnew_height = height[:]\n\t\t\t\tfor j in range(i):\n\t\t\t\t\tnew_height[idx + j] += i\n\t\t\t\tdfs(new_height, moves + 1)\n\t\tdfs([0] * m, 0)\n\t\treturn self.best\n", "class Solution:\n\n\tdef tilingRectangle(self, m: int, n: int) -> int:\n\t\tself.ans = m * n\n\n\t\tdef helper(h, res):\n\t\t\tif all((x == m for x in h)):\n\t\t\t\tself.ans = min(self.ans, res)\n\t\t\t\treturn\n\t\t\tif res >= self.ans:\n\t\t\t\treturn\n\t\t\ttemp = min(h)\n\t\t\tind = h.index(temp)\n\t\t\tr = ind + 1\n\t\t\twhile r < min(n, ind + m - temp + 1) and h[r] == temp:\n\t\t\t\tr += 1\n\t\t\tfor i in range(min(r - ind, m - temp), 0, -1):\n\t\t\t\tnew_h = h[:]\n\t\t\t\tfor j in range(ind, ind + i):\n\t\t\t\t\tnew_h[j] += i\n\t\t\t\thelper(new_h, res + 1)\n\t\thelper([0] * n, 0)\n\t\treturn self.ans\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n < m:\n\t\t\treturn self.tilingRectangle(m, n)\n\t\th = [0] * m\n\t\tself.ans = 100000\n\t\tself.dfs(n, m, h, 0)\n\t\treturn self.ans\n\n\tdef dfs(self, m, n, h, cur):\n\t\tif cur >= self.ans:\n\t\t\treturn\n\t\tmin_h = min(h)\n\t\tif min_h == m:\n\t\t\tself.ans = min(self.ans, cur)\n\t\t\treturn\n\t\tfor j in range(n):\n\t\t\tif h[j] == min_h:\n\t\t\t\tbreak\n\t\tstart = j\n\t\twhile j + 1 < n and h[j] == h[j + 1] and (j + 1 - start + 1 + h[j] <= m):\n\t\t\tj += 1\n\t\tside = j - start + 1\n\t\tfor k in reversed(range(1, side + 1)):\n\t\t\ttemp = list(h)\n\t\t\tfor j in range(start, start + k):\n\t\t\t\ttemp[j] += k\n\t\t\tself.dfs(m, n, temp, cur + 1)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tmemo = {}\n\t\treturn self.dfs(n, m, memo)\n\n\tdef dfs(self, x, y, memo):\n\t\tif x == 0 or y == 0:\n\t\t\treturn 0\n\t\tif x == y:\n\t\t\treturn 1\n\t\tif x == 1:\n\t\t\treturn y\n\t\tif y == 1:\n\t\t\treturn x\n\t\tif (x, y) in memo:\n\t\t\treturn memo[x, y]\n\t\tans = float('inf')\n\t\tfor i in range(1, x):\n\t\t\tans = min(ans, self.dfs(i, y, memo) + self.dfs(x - i, y, memo))\n\t\tfor j in range(1, y):\n\t\t\tans = min(ans, self.dfs(x, j, memo) + self.dfs(x, y - j, memo))\n\t\tfor side in range(1, min(x, y)):\n\t\t\tfor i in range(x - side):\n\t\t\t\tfor j in range(y - side):\n\t\t\t\t\tans1 = self.dfs(i, j + side, memo)\n\t\t\t\t\tans2 = self.dfs(x - i, j, memo)\n\t\t\t\t\tans3 = self.dfs(x - i - side, y - j, memo)\n\t\t\t\t\tans4 = self.dfs(i + side, y - j - side, memo)\n\t\t\t\t\tans = min(ans, ans1 + ans2 + ans3 + ans4 + 1)\n\t\tmemo[x, y] = ans\n\t\treturn memo[x, y]\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.result = n * m\n\t\theights = [0] * n\n\n\t\tdef dfs(cur):\n\t\t\tif cur >= self.result:\n\t\t\t\treturn\n\t\t\tcurMinHeight = min(heights)\n\t\t\tif curMinHeight == m:\n\t\t\t\tself.result = cur\n\t\t\t\treturn\n\t\t\tend = start = heights.index(curMinHeight)\n\t\t\twhile end < n and heights[start] == heights[end] and (end - start + 1 + curMinHeight <= m):\n\t\t\t\tend += 1\n\t\t\tfor i in range(end - 1, start - 1, -1):\n\t\t\t\tsize = i - start + 1\n\t\t\t\tfor j in range(start, i + 1):\n\t\t\t\t\theights[j] += size\n\t\t\t\tdfs(cur + 1)\n\t\t\t\tfor j in range(start, i + 1):\n\t\t\t\t\theights[j] -= size\n\t\tdfs(0)\n\t\treturn self.result\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n < m:\n\t\t\t(n, m) = (m, n)\n\t\tif m == n:\n\t\t\treturn 1\n\t\theights = [0] * n\n\t\tdp = {}\n\t\tfinal = [m * n]\n\n\t\tdef helper(heights, counts):\n\t\t\tkey = tuple(heights)\n\t\t\tif counts >= final[0]:\n\t\t\t\treturn\n\t\t\tif all((h == m for h in heights)):\n\t\t\t\tfinal[0] = min(final[0], counts)\n\t\t\t\treturn\n\t\t\tif key in dp and dp[key] <= counts:\n\t\t\t\treturn\n\t\t\tdp[key] = counts\n\t\t\tmin_val = min(heights)\n\t\t\tidx = heights.index(min_val)\n\t\t\td = 0\n\t\t\tfor i in range(idx, n):\n\t\t\t\tif heights[i] == min_val:\n\t\t\t\t\td += 1\n\t\t\t\telse:\n\t\t\t\t\tbreak\n\t\t\td = min(m - min_val, d)\n\t\t\tfor i in range(d, 0, -1):\n\t\t\t\tif heights[idx] + i <= m:\n\t\t\t\t\thelper(heights[:idx] + [heights[idx] + i] * i + heights[idx + i:], counts + 1)\n\t\t\treturn\n\t\thelper(heights, 0)\n\t\treturn final[0]\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif m == n:\n\t\t\treturn 1\n\t\tif n > m:\n\t\t\t(m, n) = (n, m)\n\t\th_i = [0] * n\n\t\tvisited = {}\n\t\tres = [m * n]\n\n\t\tdef dfs(height, cnt):\n\t\t\tif cnt > res[0]:\n\t\t\t\treturn\n\t\t\tstatus = tuple(height)\n\t\t\tif status in visited and visited[status] <= cnt:\n\t\t\t\treturn\n\t\t\tvisited[status] = cnt\n\t\t\tcomplete = True\n\t\t\tstart_j = -1\n\t\t\tlowest_h = m + 1\n\t\t\tfor j in range(n):\n\t\t\t\tif height[j] < m:\n\t\t\t\t\tcomplete = False\n\t\t\t\tif height[j] < lowest_h:\n\t\t\t\t\tstart_j = j\n\t\t\t\t\tlowest_h = height[j]\n\t\t\tif complete:\n\t\t\t\tres[0] = min(res[0], cnt)\n\t\t\t\treturn\n\t\t\tj = start_j\n\t\t\twhile j < n and height[j] == lowest_h:\n\t\t\t\tj += 1\n\t\t\tmax_l = min(j - start_j, m - lowest_h)\n\t\t\tfor l in range(max_l, 0, -1):\n\t\t\t\tnext_h = list(height)\n\t\t\t\tfor k in range(l):\n\t\t\t\t\tnext_h[start_j + k] += l\n\t\t\t\tdfs(next_h, cnt + 1)\n\t\tdfs(h_i, 0)\n\t\treturn res[0]\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n > m:\n\t\t\t(n, m) = (m, n)\n\t\tres = n * m\n\n\t\tdef dfs(heights, count, rem_area):\n\t\t\tnonlocal res\n\t\t\tif count >= res:\n\t\t\t\treturn\n\t\t\t(lowest_idx, lowest_height, width, prev) = (-1, math.inf, 0, -1)\n\t\t\tfor i in range(m):\n\t\t\t\tif heights[i] < lowest_height:\n\t\t\t\t\t(lowest_height, lowest_idx, width, prev) = (heights[i], i, 1, i)\n\t\t\t\telif heights[i] == lowest_height and prev == i - 1:\n\t\t\t\t\t(width, prev) = (width + 1, i)\n\t\t\tif rem_area == 0:\n\t\t\t\tres = min(res, count)\n\t\t\t\treturn\n\t\t\twidth = min(width, n - lowest_height)\n\t\t\tfor w in range(width, 0, -1):\n\t\t\t\ttemp = heights.copy()\n\t\t\t\tfor j in range(lowest_idx, lowest_idx + w):\n\t\t\t\t\ttemp[j] += w\n\t\t\t\tdfs(temp, count + 1, rem_area - w * w)\n\t\tdfs([0] * m, 0, n * m)\n\t\treturn res\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.res = n * m\n\n\t\tdef dfs(heights, moves):\n\t\t\tif min(heights) == m:\n\t\t\t\tself.res = min(self.res, moves)\n\t\t\t\treturn\n\t\t\tif moves == self.res:\n\t\t\t\treturn\n\t\t\tminh = min(heights)\n\t\t\tleft = right = heights.index(minh)\n\t\t\twhile right < n and heights[right] == minh:\n\t\t\t\tright += 1\n\t\t\tfor size in range(min(m - minh, right - left), 0, -1):\n\t\t\t\tnewh = heights[:]\n\t\t\t\tfor i in range(size):\n\t\t\t\t\tnewh[left + i] += size\n\t\t\t\tdfs(newh, moves + 1)\n\t\tdfs([0] * n, 0)\n\t\treturn self.res\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.best = n * m\n\n\t\tdef dfs(hts, mvs):\n\t\t\tif mvs >= self.best:\n\t\t\t\treturn\n\t\t\tif all((h == n for h in hts)):\n\t\t\t\tself.best = min(self.best, mvs)\n\t\t\t\treturn\n\t\t\ti = min(list(range(m)), key=lambda i: hts[i])\n\t\t\tj = i + ([hts[k] != hts[i] for k in range(i, m)] + [True]).index(True)\n\t\t\tfor x in range(min(j - i, n - hts[i]), 0, -1):\n\t\t\t\tfor k in range(x):\n\t\t\t\t\thts[i + k] += x\n\t\t\t\tdfs(hts, mvs + 1)\n\t\t\t\tfor k in range(x):\n\t\t\t\t\thts[i + k] -= x\n\t\tdfs([0] * m, 0)\n\t\treturn self.best\n", "class Solution:\n\n\tdef tilingRectangle(self, m, n):\n\t\tself.best = n * m\n\n\t\tdef dfs(heights, mvs):\n\t\t\tif mvs >= self.best:\n\t\t\t\treturn\n\t\t\tif all((h == n for h in heights)):\n\t\t\t\tself.best = min(self.best, mvs)\n\t\t\t\treturn\n\t\t\ti = j = min(list(range(m)), key=lambda i: heights[i])\n\t\t\twhile j < m and heights[j] == heights[i]:\n\t\t\t\tj += 1\n\t\t\tfor x in range(min(j - i, n - heights[i]), 0, -1):\n\t\t\t\tdfs(heights[:i] + [heights[i] + x] * x + heights[i + x:], mvs + 1)\n\t\theights = [0] * m\n\t\tdfs(heights, 0)\n\t\treturn self.best\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif m == n:\n\t\t\treturn 1\n\t\tif n < m:\n\t\t\t(m, n) = (n, m)\n\t\tif m == 1:\n\t\t\treturn n\n\t\tif m == 2:\n\t\t\t(k, rem) = divmod(n, 2)\n\t\t\treturn k + 2 * rem\n\n\t\tdef recurse(h, ct):\n\t\t\tnonlocal Min\n\t\t\tif ct >= Min:\n\t\t\t\treturn\n\t\t\tif all((x == m for x in h)):\n\t\t\t\tMin = min(Min, ct)\n\t\t\t\treturn\n\t\t\ti = j = min(list(range(n)), key=lambda c: h[c])\n\t\t\thi = h[i]\n\t\t\tbound = min(n, i + m - hi)\n\t\t\twhile j < bound and h[j] == hi:\n\t\t\t\tj += 1\n\t\t\tfor x in range(j - i, 0, -1):\n\t\t\t\trecurse(h[:i] + [hi + x] * x + h[i + x:], ct + 1)\n\t\tMin = m * n\n\t\trecurse([0] * n, 0)\n\t\treturn Min\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.result = n * m\n\n\t\tdef dfs(heights, moves):\n\t\t\tif moves > self.result:\n\t\t\t\treturn\n\t\t\tif all((h == n for h in heights)):\n\t\t\t\tself.result = min(self.result, moves)\n\t\t\t\treturn\n\t\t\tmin_height = min(heights)\n\t\t\tidx = heights.index(min_height)\n\t\t\tright_boundary = idx + 1\n\t\t\twhile right_boundary < m and heights[right_boundary] == min_height:\n\t\t\t\tright_boundary += 1\n\t\t\tfor i in range(min(right_boundary - idx, n - min_height), 0, -1):\n\t\t\t\tdfs(heights[:idx] + [min_height + i] * i + heights[idx + i:], moves + 1)\n\t\tdfs([0] * m, 0)\n\t\treturn self.result\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int):\n\t\tcache = [[-1 for i in range(m + 1)] for j in range(n + 1)]\n\t\treturn self.helper(n, m, cache)\n\n\tdef helper(self, n: int, m: int, cache) -> int:\n\t\tif n <= 0 or m <= 0:\n\t\t\treturn 0\n\t\tif n == 11 and m == 13 or (n == 13 and m == 11):\n\t\t\treturn 6\n\t\tif n == m:\n\t\t\treturn 1\n\t\tif cache[n][m] != -1:\n\t\t\treturn cache[n][m]\n\t\trr1 = 10000\n\t\trr2 = 10000\n\t\t_min = 10000\n\t\tfor x in range(1, min(n, m) + 1):\n\t\t\trr1 = self.helper(n, m - x, cache) + self.helper(n - x, x, cache)\n\t\t\trr2 = self.helper(n - x, m, cache) + self.helper(x, m - x, cache)\n\t\t\t_min = min(rr1, min(rr2, _min))\n\t\tcache[n][m] = _min + 1\n\t\treturn _min + 1\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n == m:\n\t\t\treturn 1\n\t\tif n > m:\n\t\t\t(n, m) = (m, n)\n\t\tlayers0 = [0 for _ in range(n)]\n\t\tvisited = {}\n\t\tans = [n * m]\n\n\t\tdef dfs(layers, stepsNow):\n\t\t\tif stepsNow > ans[0]:\n\t\t\t\treturn\n\t\t\tkey = tuple(layers)\n\t\t\tif key in visited and stepsNow >= visited[key]:\n\t\t\t\treturn\n\t\t\tvisited[key] = stepsNow\n\t\t\tminH = m + 1\n\t\t\ti0 = -1\n\t\t\tfor (i, h) in enumerate(layers):\n\t\t\t\tif h < minH:\n\t\t\t\t\tminH = h\n\t\t\t\t\ti0 = i\n\t\t\tif minH == m:\n\t\t\t\tans[0] = min(ans[0], stepsNow)\n\t\t\t\treturn\n\t\t\tminHWidth = 0\n\t\t\tmaxL = m - minH\n\t\t\tfor i in range(i0, n):\n\t\t\t\tif layers[i] == minH:\n\t\t\t\t\tminHWidth += 1\n\t\t\t\telse:\n\t\t\t\t\tbreak\n\t\t\tmaxL = min(maxL, minHWidth)\n\t\t\tfor l in range(maxL, 0, -1):\n\t\t\t\tnextLayers = list(key)\n\t\t\t\tfor i in range(i0, i0 + l):\n\t\t\t\t\tnextLayers[i] += l\n\t\t\t\tdfs(nextLayers, stepsNow + 1)\n\t\t\treturn\n\t\tdfs(layers0, 0)\n\t\treturn ans[0]\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\th = [0] * m\n\t\tself.ans = m * n\n\n\t\tdef dfs(h: List[int], cur: int) -> None:\n\t\t\tmin_h = min(h)\n\t\t\tif min_h == n:\n\t\t\t\tself.ans = min(self.ans, cur)\n\t\t\t\treturn\n\t\t\tif cur > self.ans:\n\t\t\t\treturn\n\t\t\tidx = h.index(min_h)\n\t\t\tj = idx\n\t\t\twhile j < len(h) and h[j] == min_h:\n\t\t\t\tj += 1\n\t\t\tfill_width = j - idx\n\t\t\tfill_height = n - min_h\n\t\t\tfor fill in range(min(fill_width, fill_height), 0, -1):\n\t\t\t\tfor k in range(idx, idx + fill):\n\t\t\t\t\th[k] += fill\n\t\t\t\tdfs(h, cur + 1)\n\t\t\t\tfor k in range(idx, idx + fill):\n\t\t\t\t\th[k] -= fill\n\t\tdfs(h, 0)\n\t\treturn self.ans\n", "class Solution:\n\tres = float('inf')\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\ts = {}\n\n\t\tdef dfs(n, m, h, cnt):\n\t\t\tif cnt > self.res:\n\t\t\t\treturn\n\t\t\tis_full = True\n\t\t\tpos = -1\n\t\t\tminh = float('inf')\n\t\t\tfor i in range(1, n + 1):\n\t\t\t\tif h[i] < m:\n\t\t\t\t\tis_full = False\n\t\t\t\tif h[i] < minh:\n\t\t\t\t\tpos = i\n\t\t\t\t\tminh = h[i]\n\t\t\tif is_full:\n\t\t\t\tself.res = min(cnt, self.res)\n\t\t\t\treturn\n\t\t\tkey = 0\n\t\t\tbase = m + 1\n\t\t\tfor i in range(1, n + 1):\n\t\t\t\tkey += h[i] * base\n\t\t\t\tbase *= m + 1\n\t\t\tif key in s and s[key] <= cnt:\n\t\t\t\treturn\n\t\t\ts[key] = cnt\n\t\t\tend = pos\n\t\t\twhile end < n and h[end + 1] == h[pos] and (end + 1 - pos + 1 + minh <= m):\n\t\t\t\tend += 1\n\t\t\tfor j in range(end, pos - 1, -1):\n\t\t\t\tcurh = j - pos + 1\n\t\t\t\tnex = h[:]\n\t\t\t\tfor k in range(pos, j + 1):\n\t\t\t\t\tnex[k] += curh\n\t\t\t\tdfs(n, m, nex, cnt + 1)\n\t\tif n == m:\n\t\t\treturn 1\n\t\tif n > m:\n\t\t\t(n, m) = (m, n)\n\t\tdfs(n, m, [0] * (n + 1), 0)\n\t\treturn self.res\n", "from collections import defaultdict\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\trow = tuple([m] * n)\n\n\t\tdef valid(row, i, side):\n\t\t\treturn i + side <= len(row) and all((h >= side for h in row[i:i + side]))\n\t\tdp = defaultdict(int)\n\n\t\tdef count(row, i):\n\t\t\tif i >= len(row):\n\t\t\t\treturn 0\n\t\t\tif row in dp:\n\t\t\t\treturn dp[row]\n\t\t\tres = float('inf')\n\t\t\tside = 1\n\t\t\twhile valid(row, i, side):\n\t\t\t\tnrow = list(row)\n\t\t\t\tfor j in range(i, i + side):\n\t\t\t\t\tnrow[j] -= side\n\t\t\t\tni = i\n\t\t\t\twhile ni < len(row) and (not nrow[ni]):\n\t\t\t\t\tni += 1\n\t\t\t\tres = min(res, 1 + count(tuple(nrow), ni))\n\t\t\t\tside += 1\n\t\t\tdp[row] = res\n\t\t\treturn res\n\t\treturn count(row, 0)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tans = math.inf\n\t\tmatrix = [[0] * m for _ in range(n)]\n\n\t\tdef dfs(r, c, count):\n\t\t\tnonlocal ans\n\t\t\tif count >= ans:\n\t\t\t\treturn\n\t\t\tif r >= n:\n\t\t\t\tans = count\n\t\t\t\treturn\n\t\t\tif c >= m:\n\t\t\t\tdfs(r + 1, 0, count)\n\t\t\t\treturn\n\t\t\tif matrix[r][c]:\n\t\t\t\tdfs(r, c + 1, count)\n\t\t\t\treturn\n\t\t\tfor i in range(min(n - r, m - c), 0, -1):\n\t\t\t\tif not check(r, c, i):\n\t\t\t\t\tbreak\n\t\t\t\tcover(r, c, i)\n\t\t\t\tdfs(r, c + i, count + 1)\n\t\t\t\tuncover(r, c, i)\n\n\t\tdef check(r, c, k):\n\t\t\treturn all((matrix[i][j] == 0 for i in range(r, r + k) for j in range(c, c + k)))\n\n\t\tdef cover(r, c, k):\n\t\t\tfor i in range(r, r + k):\n\t\t\t\tfor j in range(c, c + k):\n\t\t\t\t\tmatrix[i][j] = 1\n\n\t\tdef uncover(r, c, k):\n\t\t\tfor i in range(r, r + k):\n\t\t\t\tfor j in range(c, c + k):\n\t\t\t\t\tmatrix[i][j] = 0\n\t\tdfs(0, 0, 0)\n\t\treturn ans\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tmemo = {}\n\n\t\tdef helper(w, h):\n\t\t\tif w > h:\n\t\t\t\t(w, h) = (h, w)\n\t\t\tif (w, h) not in memo:\n\t\t\t\tif w == h:\n\t\t\t\t\tans = 1\n\t\t\t\telif w == 1:\n\t\t\t\t\tans = h\n\t\t\t\telif w == 0:\n\t\t\t\t\tans = 0\n\t\t\t\telse:\n\t\t\t\t\tans = w * h\n\t\t\t\t\tfor iw in range(1, w // 2 + 1):\n\t\t\t\t\t\tans = min(ans, helper(iw, h) + helper(w - iw, h))\n\t\t\t\t\tfor ih in range(1, h // 2 + 1):\n\t\t\t\t\t\tans = min(ans, helper(w, ih) + helper(w, h - ih))\n\t\t\t\t\tfor iw in range(1, (w + 1) // 2):\n\t\t\t\t\t\tfor ih in range(1, (h + 1) // 2):\n\t\t\t\t\t\t\tfor s in range(1, min(w - 2 * iw, h - 2 * ih) + 1):\n\t\t\t\t\t\t\t\tans = min(ans, 1 + helper(iw + s, ih) + helper(w - iw - s, ih + s) + helper(w - iw, h - ih - s) + helper(iw, h - ih))\n\t\t\t\tmemo[w, h] = ans\n\t\t\treturn memo[w, h]\n\t\treturn helper(n, m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n > m:\n\t\t\tself.tilingRectangle(m, n)\n\t\tself.ans = n * m\n\t\th = [0] * n\n\t\tself.dfs(h, 0, n, m)\n\t\treturn self.ans\n\n\tdef dfs(self, h, cur, n, m):\n\t\tif cur >= self.ans:\n\t\t\treturn\n\t\tmin_h = min(h)\n\t\tif min_h == m:\n\t\t\tself.ans = cur\n\t\t\treturn\n\t\tfor i in range(n):\n\t\t\tif h[i] == min_h:\n\t\t\t\tbreak\n\t\t(start, end) = (i, i)\n\t\twhile end < n and h[start] == h[end] and (end - start + 1 + min_h <= m):\n\t\t\tend += 1\n\t\tfor i in reversed(list(range(start, end))):\n\t\t\tsize = i - start + 1\n\t\t\tfor j in range(start, i + 1):\n\t\t\t\th[j] += size\n\t\t\tself.dfs(h, cur + 1, n, m)\n\t\t\tfor j in range(start, i + 1):\n\t\t\t\th[j] -= size\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tfrom functools import lru_cache\n\n\t\t@lru_cache(None)\n\t\tdef dp(n, m):\n\t\t\t(p, q) = (min(n, m), max(n, m))\n\t\t\tif p == 0:\n\t\t\t\treturn 0\n\t\t\tif p == 1:\n\t\t\t\treturn q\n\t\t\tif q % p == 0:\n\t\t\t\treturn q // p\n\t\t\tminunits = p * q\n\t\t\tfor r in range(1, p):\n\t\t\t\tminunits = min(minunits, 1 + dp(p - r, r) + dp(p, q - r))\n\t\t\t\tminunits = min(minunits, 1 + dp(q - r, r) + dp(q, p - r))\n\t\t\tfor cl in range(1, n):\n\t\t\t\tfor cr in range(1, n - cl):\n\t\t\t\t\tfor rl in range(1, m):\n\t\t\t\t\t\tfor rr in range(1, m - rl):\n\t\t\t\t\t\t\tminunits = min(minunits, dp(rl, n - cr) + dp(m - rl, cl) + dp(n - cl, rr) + dp(m - rr, cr) + dp(n - cl - cr, m - rl - rr))\n\t\t\treturn minunits\n\t\treturn dp(n, m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n > m:\n\t\t\t(n, m) = (m, n)\n\t\tif m == n:\n\t\t\treturn 1\n\t\tres = [m * n]\n\t\tdp = {}\n\n\t\tdef dfs(cnt, hs):\n\t\t\tif cnt > res[0]:\n\t\t\t\treturn\n\t\t\tkey = tuple(hs)\n\t\t\tif key in dp and dp[key] <= cnt:\n\t\t\t\treturn\n\t\t\tdp[key] = cnt\n\t\t\tif all((h == n for h in hs)):\n\t\t\t\tres[0] = min(res[0], cnt)\n\t\t\t\treturn\n\t\t\tmin_h = min(hs)\n\t\t\tmin_i = hs.index(min_h)\n\t\t\tr = m\n\t\t\tfor i in range(min_i, m):\n\t\t\t\tif hs[i] > min_h:\n\t\t\t\t\tr = i\n\t\t\t\t\tbreak\n\t\t\tfor side in range(min(r - min_i, n - min_h), 0, -1):\n\t\t\t\tdfs(cnt + 1, hs[:min_i] + [side + min_h] * side + hs[min_i + side:])\n\t\tdfs(0, [0] * m)\n\t\treturn res[0]\n", "from functools import lru_cache\n\nclass Solution:\n\n\t@lru_cache(None)\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\t(n, m) = (min(n, m), max(n, m))\n\t\tif m == n:\n\t\t\treturn 1\n\t\tif m % n == 0:\n\t\t\treturn m // n\n\t\ts1 = m * n\n\t\tfor x in range(1, m // 2 + 1):\n\t\t\ts1 = min(s1, self.tilingRectangle(n, x) + self.tilingRectangle(n, m - x))\n\t\tfor y in range(1, n // 2 + 1):\n\t\t\ts1 = min(s1, self.tilingRectangle(y, m) + self.tilingRectangle(n - y, m))\n\t\ts2 = m * n\n\t\tfor xL in range(1, m // 2 + 1):\n\t\t\tfor xR in range(1, m - xL):\n\t\t\t\tfor yL in range(1, n // 2 + 1):\n\t\t\t\t\tfor yR in range(1, n - yL):\n\t\t\t\t\t\ts2 = min(s2, self.tilingRectangle(n - yR, xL) + self.tilingRectangle(yL, m - xL) + self.tilingRectangle(n - yL, xR) + self.tilingRectangle(yR, m - xR) + self.tilingRectangle(n - yL - yR, m - xL - xR))\n\t\treturn min(s1, s2)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif m > n:\n\t\t\t(n, m) = (m, n)\n\t\t(res, state) = (m * n, [0] * n)\n\n\t\tdef dfs(count):\n\t\t\tnonlocal res\n\t\t\tif count > res:\n\t\t\t\treturn\n\t\t\tmin_h = min(state)\n\t\t\tif min_h == m:\n\t\t\t\tres = min(res, count)\n\t\t\t\treturn\n\t\t\te = s = state.index(min_h)\n\t\t\twhile e < n and state[e] == min_h:\n\t\t\t\te += 1\n\t\t\tmax_len = min(e - s, m - min_h)\n\t\t\tfor l in range(max_len, 0, -1):\n\t\t\t\tfor i in range(s, s + l):\n\t\t\t\t\tstate[i] += l\n\t\t\t\tdfs(count + 1)\n\t\t\t\tfor i in range(s, s + l):\n\t\t\t\t\tstate[i] -= l\n\t\tdfs(0)\n\t\treturn res\n", "class Solution:\n\n\tdef tilingRectangle(self, R, C):\n\t\tA = [[0] * C for _ in range(R)]\n\t\tself.ans = R * C\n\n\t\tdef search(r, c, steps):\n\t\t\tif steps >= self.ans:\n\t\t\t\treturn\n\t\t\tif r == R:\n\t\t\t\tself.ans = steps\n\t\t\t\treturn\n\t\t\tif c == C:\n\t\t\t\treturn search(r + 1, 0, steps)\n\t\t\tif A[r][c]:\n\t\t\t\treturn search(r, c + 1, steps)\n\t\t\tfor k in range(min(R - r, C - c), 0, -1):\n\t\t\t\tbad = False\n\t\t\t\tfor r0 in range(r, r + k):\n\t\t\t\t\tfor c0 in range(c, c + k):\n\t\t\t\t\t\tif A[r0][c0]:\n\t\t\t\t\t\t\tbad = True\n\t\t\t\t\t\t\tbreak\n\t\t\t\t\tif bad:\n\t\t\t\t\t\tbreak\n\t\t\t\tif not bad:\n\t\t\t\t\tfor r0 in range(r, r + k):\n\t\t\t\t\t\tfor c0 in range(c, c + k):\n\t\t\t\t\t\t\tA[r0][c0] = 1\n\t\t\t\t\tsearch(r, c + 1, steps + 1)\n\t\t\t\t\tfor r0 in range(r, r + k):\n\t\t\t\t\t\tfor c0 in range(c, c + k):\n\t\t\t\t\t\t\tA[r0][c0] = 0\n\t\tsearch(0, 0, 0)\n\t\treturn self.ans\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.res = math.inf\n\t\tgrid = [[False] * n for _ in range(m)]\n\n\t\tdef dfs(i, j, s):\n\t\t\tif s >= self.res:\n\t\t\t\treturn\n\t\t\telif i == m:\n\t\t\t\tself.res = s\n\t\t\telif j == n:\n\t\t\t\tdfs(i + 1, 0, s)\n\t\t\telif grid[i][j]:\n\t\t\t\tdfs(i, j + 1, s)\n\t\t\telse:\n\t\t\t\tside = min(m - i, n - j)\n\t\t\t\twhile side:\n\t\t\t\t\tif not any((grid[ni][nj] for ni in range(i, i + side) for nj in range(j, j + side))):\n\t\t\t\t\t\tfor ni in range(i, i + side):\n\t\t\t\t\t\t\tfor nj in range(j, j + side):\n\t\t\t\t\t\t\t\tgrid[ni][nj] = True\n\t\t\t\t\t\tdfs(i, j + side, s + 1)\n\t\t\t\t\t\tfor ni in range(i, i + side):\n\t\t\t\t\t\t\tfor nj in range(j, j + side):\n\t\t\t\t\t\t\t\tgrid[ni][nj] = False\n\t\t\t\t\tside -= 1\n\t\tdfs(0, 0, 0)\n\t\treturn self.res\n", "from math import inf\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\trec = [[False] * n for _ in range(m)]\n\t\tres = inf\n\n\t\tdef is_avail(r, c, k):\n\t\t\treturn all((not rec[i][j] for i in range(r, r + k) for j in range(c, c + k)))\n\n\t\tdef update(r, c, k, val):\n\t\t\tfor i in range(r, r + k):\n\t\t\t\tfor j in range(c, c + k):\n\t\t\t\t\trec[i][j] = val\n\n\t\tdef dfs(r, c, cnt):\n\t\t\tnonlocal res\n\t\t\tif r == m:\n\t\t\t\tres = min(res, cnt)\n\t\t\t\treturn\n\t\t\tif c == n:\n\t\t\t\tdfs(r + 1, 0, cnt)\n\t\t\t\treturn\n\t\t\tif rec[r][c]:\n\t\t\t\tdfs(r, c + 1, cnt)\n\t\t\t\treturn\n\t\t\tif cnt >= res:\n\t\t\t\treturn\n\t\t\tmax_tile = min(m - r, n - c)\n\t\t\tfor k in range(max_tile, 0, -1):\n\t\t\t\tif is_avail(r, c, k):\n\t\t\t\t\tupdate(r, c, k, True)\n\t\t\t\t\tdfs(r, c + k, cnt + 1)\n\t\t\t\t\tupdate(r, c, k, False)\n\t\tdfs(0, 0, 0)\n\t\treturn res\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tdp = {}\n\t\tif n < m:\n\t\t\t(m, n) = (n, m)\n\t\tif m == n:\n\t\t\treturn 1\n\t\tres = [m * n + 1]\n\n\t\tdef dfs(ys, cnt):\n\t\t\tkey = tuple(ys)\n\t\t\tif key not in dp or cnt < dp[key]:\n\t\t\t\tdp[key] = cnt\n\t\t\tif dp[key] < cnt or cnt > res[0]:\n\t\t\t\treturn\n\t\t\tif all((i == m for i in ys)):\n\t\t\t\tres[0] = min(res[0], cnt)\n\t\t\t\treturn\n\t\t\tif any((i > m for i in ys)):\n\t\t\t\treturn\n\t\t\tymin = min(ys)\n\t\t\tidx = ys.index(ymin)\n\t\t\tymax = 0\n\t\t\tfor i in range(idx, n):\n\t\t\t\tif ys[i] > ymin:\n\t\t\t\t\tbreak\n\t\t\t\telse:\n\t\t\t\t\tymax += 1\n\t\t\tymax = min(ymax, m)\n\t\t\tfor i in range(ymax, 0, -1):\n\t\t\t\tdfs(ys[:idx] + [ys[idx] + i] * i + ys[idx + i:], cnt + 1)\n\t\tdfs([0] * n, 0)\n\t\treturn res[0]\n", "from functools import lru_cache\nimport numpy as np\n\nclass Solution:\n\n\tdef __init__(self):\n\t\tself.cache = {}\n\t\tself.res = np.inf\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\tdef tilingRectangleCalc(state, cnt):\n\t\t\tif cnt > self.res:\n\t\t\t\treturn\n\t\t\tstate = list(state)\n\t\t\tminHeight = min(state)\n\t\t\tif minHeight == n:\n\t\t\t\tself.res = min(self.res, cnt)\n\t\t\t\treturn\n\t\t\tminIdx = state.index(minHeight)\n\t\t\tmaxL = 1\n\t\t\twhile minIdx + maxL - 1 <= m - 1 and state[minIdx + maxL - 1] == minHeight:\n\t\t\t\tmaxL += 1\n\t\t\tfor l in range(maxL - 1, 0, -1):\n\t\t\t\tif minHeight + l > n:\n\t\t\t\t\tcontinue\n\t\t\t\ts = tuple(state[:minIdx] + [minHeight + l] * l + state[minIdx + l:])\n\t\t\t\tif s in self.cache and self.cache[s] < cnt + 1:\n\t\t\t\t\tcontinue\n\t\t\t\tself.cache[s] = cnt + 1\n\t\t\t\ttilingRectangleCalc(s, cnt + 1)\n\t\t\treturn\n\t\tif m > n:\n\t\t\t(n, m) = (m, n)\n\t\ttilingRectangleCalc(tuple([0] * m), 0)\n\t\treturn self.res\n", "class Solution:\n\n\tdef tilingRectangle(self, m: int, n: int) -> int:\n\t\tcur = [0] * (n * m)\n\t\tq = [cur]\n\t\tstep = 0\n\t\tseen = {tuple(cur)}\n\t\twhile q and step < n * m + 1:\n\t\t\tstep += 1\n\t\t\tnex = []\n\t\t\tfor cur in q:\n\t\t\t\tfound = True\n\t\t\t\tfor i in range(m):\n\t\t\t\t\tfor j in range(n):\n\t\t\t\t\t\tif cur[i * n + j] == 0:\n\t\t\t\t\t\t\tstart = [i, j]\n\t\t\t\t\t\t\tfound = False\n\t\t\t\t\t\t\tbreak\n\t\t\t\t\tif not found:\n\t\t\t\t\t\tbreak\n\t\t\t\tif found:\n\t\t\t\t\treturn step - 1\n\t\t\t\twhile j + 1 < n and cur[i * n + j + 1] == 0:\n\t\t\t\t\tj += 1\n\t\t\t\tk = j - start[1] + 1\n\t\t\t\tfor sz in range(1, k + 1):\n\t\t\t\t\tcc = cur.copy()\n\t\t\t\t\tflag = False\n\t\t\t\t\tfor i in range(start[0], start[0] + sz):\n\t\t\t\t\t\tfor j in range(start[1], start[1] + sz):\n\t\t\t\t\t\t\tif not (0 <= i < m and 0 <= j < n and (cur[i * n + j] == 0)):\n\t\t\t\t\t\t\t\tflag = True\n\t\t\t\t\t\t\t\tbreak\n\t\t\t\t\t\t\tcc[i * n + j] = 1\n\t\t\t\t\t\tif flag:\n\t\t\t\t\t\t\tbreak\n\t\t\t\t\tif flag:\n\t\t\t\t\t\tbreak\n\t\t\t\t\tC = tuple(cc)\n\t\t\t\t\tif C not in seen:\n\t\t\t\t\t\tseen.add(C)\n\t\t\t\t\t\tnex.append(cc)\n\t\t\tq = nex\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.n = n\n\t\tself.m = m\n\t\tboard = [[0] * n for _ in range(m)]\n\t\tself.res = float('inf')\n\t\tself.dfs(board, 0)\n\t\treturn self.res\n\n\tdef dfs(self, board, count):\n\t\tif count >= self.res:\n\t\t\treturn\n\t\t(i, j) = self.find_next(board)\n\t\tif i == -1 and j == -1:\n\t\t\tself.res = min(self.res, count)\n\t\t\treturn\n\t\tmax_length = self.find_max_length(board, i, j)\n\t\tfor k in range(1, max_length + 1)[::-1]:\n\t\t\tself.assign(board, i, j, k, 1)\n\t\t\tself.dfs(board, count + 1)\n\t\t\tself.assign(board, i, j, k, 0)\n\n\tdef assign(self, board, i, j, length, val):\n\t\tfor row in range(i, i + length):\n\t\t\tfor col in range(j, j + length):\n\t\t\t\tboard[row][col] = val\n\n\tdef find_max_length(self, board, i, j):\n\t\tmax_length = 1\n\t\twhile i + max_length - 1 < self.m and j + max_length - 1 < self.n:\n\t\t\tfor row in range(i, i + max_length):\n\t\t\t\tif board[row][j + max_length - 1] != 0:\n\t\t\t\t\treturn max_length - 1\n\t\t\tfor col in range(j, j + max_length):\n\t\t\t\tif board[i + max_length - 1][col] != 0:\n\t\t\t\t\treturn max_length - 1\n\t\t\tmax_length += 1\n\t\treturn max_length - 1\n\n\tdef find_next(self, board):\n\t\tfor i in range(self.m):\n\t\t\tfor j in range(self.n):\n\t\t\t\tif board[i][j] == 0:\n\t\t\t\t\treturn (i, j)\n\t\treturn (-1, -1)\n", "import math\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tgrid = [[0 for _ in range(m)] for _ in range(n)]\n\n\t\tdef try_place(i: int, j: int, l: int) -> bool:\n\t\t\tok = True\n\t\t\t(xb, yb) = (None, None)\n\t\t\tfor x in range(i, i + l):\n\t\t\t\tfor y in range(j, j + l):\n\t\t\t\t\tif grid[x][y] == 1:\n\t\t\t\t\t\tok = False\n\t\t\t\t\t\t(xb, yb) = (x, y)\n\t\t\t\t\t\tbreak\n\t\t\t\t\tgrid[x][y] = 1\n\t\t\t\tif not ok:\n\t\t\t\t\tbreak\n\t\t\tif not ok:\n\t\t\t\tdone = False\n\t\t\t\tfor x in range(i, i + l):\n\t\t\t\t\tfor y in range(j, j + l):\n\t\t\t\t\t\tif (x, y) == (xb, yb):\n\t\t\t\t\t\t\tdone = True\n\t\t\t\t\t\t\tbreak\n\t\t\t\t\t\tgrid[x][y] = 0\n\t\t\t\t\tif done:\n\t\t\t\t\t\tbreak\n\t\t\treturn ok\n\n\t\tdef un_place(i: int, j: int, l: int):\n\t\t\tfor x in range(i, i + l):\n\t\t\t\tfor y in range(j, j + l):\n\t\t\t\t\tgrid[x][y] = 0\n\n\t\tdef search(i: int, j: int, sofar: int, ans: list):\n\t\t\tif sofar >= ans[0]:\n\t\t\t\treturn\n\t\t\tif j == m:\n\t\t\t\tans[0] = min(ans[0], sofar)\n\t\t\t\treturn\n\t\t\tif i == n:\n\t\t\t\tsearch(0, j + 1, sofar, ans)\n\t\t\t\treturn\n\t\t\tif grid[i][j] == 1:\n\t\t\t\tsearch(i + 1, j, sofar, ans)\n\t\t\t\treturn\n\t\t\tfor l in reversed(range(1, min(n - i + 1, m - j + 1))):\n\t\t\t\tif try_place(i, j, l):\n\t\t\t\t\tsearch(i + 1, j, sofar + 1, ans)\n\t\t\t\t\tun_place(i, j, l)\n\t\tif len(grid) == len(grid[0]):\n\t\t\treturn 1\n\t\tans = [math.inf]\n\t\tsearch(0, 0, 0, ans)\n\t\treturn ans[0]\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.best = m * n\n\t\theight = [0] * m\n\n\t\tdef dfs(moves):\n\t\t\tif all((h == n for h in height)):\n\t\t\t\tself.best = min(self.best, moves)\n\t\t\t\treturn\n\t\t\tif moves >= self.best:\n\t\t\t\treturn\n\t\t\tidx = height.index(min(height))\n\t\t\tfor i in range(min(m - idx, n - height[idx]), 0, -1):\n\t\t\t\tfor j in range(i):\n\t\t\t\t\theight[idx + j] += i\n\t\t\t\tdfs(moves + 1)\n\t\t\t\tfor j in range(i):\n\t\t\t\t\theight[idx + j] -= i\n\t\tdfs(0)\n\t\treturn self.best\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.ans = n * m\n\n\t\tdef helper(heights, moves):\n\t\t\tif all((height == n for height in heights)):\n\t\t\t\tself.ans = min(self.ans, moves)\n\t\t\t\treturn None\n\t\t\tif moves >= self.ans:\n\t\t\t\treturn None\n\t\t\tmin_height = min(heights)\n\t\t\tmin_height_idx = heights.index(min_height)\n\t\t\tright_idx = min_height_idx + 1\n\t\t\twhile right_idx < m and heights[right_idx] == min_height:\n\t\t\t\tright_idx += 1\n\t\t\tfor idx in range(min(n - min_height, right_idx - min_height_idx), -1, -1):\n\t\t\t\tnew_heights = heights[:]\n\t\t\t\tfor next_idx in range(idx):\n\t\t\t\t\tnew_heights[min_height_idx + next_idx] += idx\n\t\t\t\thelper(new_heights, moves + 1)\n\t\thelper([0] * m, 0)\n\t\treturn self.ans\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n == m:\n\t\t\treturn 1\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\n\t\t@lru_cache(None)\n\t\tdef helper(skyline):\n\t\t\tif all((h == n for h in skyline)):\n\t\t\t\treturn 0\n\t\t\tans = float('inf')\n\t\t\tminh = min(skyline)\n\t\t\tl = skyline.index(minh)\n\t\t\tfor r in range(l, m):\n\t\t\t\tif skyline[r] != minh:\n\t\t\t\t\tbreak\n\t\t\t\tif r - l + 1 > n - minh:\n\t\t\t\t\tbreak\n\t\t\t\tnewsl = list(skyline)\n\t\t\t\tfor i in range(l, r + 1):\n\t\t\t\t\tnewsl[i] += r - l + 1\n\t\t\t\tans = min(ans, helper(tuple(newsl)))\n\t\t\treturn ans + 1\n\t\tans = helper(tuple([0] * m))\n\t\treturn ans\n", "class Solution:\n\n\tdef findSum(self, n, m, k):\n\t\tres = []\n\t\ts = m * n\n\t\thi = min(n, m)\n\t\tborder = max(n, m)\n\t\tpath = [1] * k\n\t\twhile path[0] <= hi:\n\t\t\ti = k - 1\n\t\t\twhile i >= 0 and path[i] >= hi:\n\t\t\t\ti -= 1\n\t\t\tif i == -1 or path[i] >= hi:\n\t\t\t\treturn res\n\t\t\tpath[i] += 1\n\t\t\tpath[i + 1:] = [path[i]] * (k - i - 1)\n\t\t\tif path[k - 1] + path[k - 2] > border:\n\t\t\t\tpath[i:] = [hi] * (k - i)\n\t\t\t\tcontinue\n\t\t\tif sum((x * x for x in path)) == s:\n\t\t\t\tx = path[:]\n\t\t\t\tx.reverse()\n\t\t\t\tres.append(x)\n\t\treturn res\n\n\tdef hasNoOverLap(self, x1, y1, s1, x2, y2, s2):\n\t\tif x1 + s1 - 1 < x2 or y1 + s1 - 1 < y2 or x2 + s2 - 1 < x1 or (y2 + s2 - 1 < y1):\n\t\t\treturn True\n\t\telse:\n\t\t\treturn False\n\n\tdef nextPos(self, placement, n, m, size):\n\t\tif not placement:\n\t\t\treturn (0, 0)\n\t\tfor i in range(n - size + 1):\n\t\t\tfor j in range(m - size + 1):\n\t\t\t\tif all((self.hasNoOverLap(i, j, size, x, y, z) for (x, y, z) in placement)):\n\t\t\t\t\treturn (i, j)\n\t\treturn (-1, -1)\n\n\tdef canPlace(self, sizes, n, m, placement, memo):\n\t\tif len(sizes) == 0:\n\t\t\treturn True\n\t\th = tuple(placement)\n\t\tif h in memo:\n\t\t\treturn memo[h]\n\t\tfor (k, s) in enumerate(sizes):\n\t\t\t(i, j) = self.nextPos(placement, n, m, s)\n\t\t\tif i == -1:\n\t\t\t\tcontinue\n\t\t\tplacement.append((i, j, s))\n\t\t\tif self.canPlace(sizes[:k] + sizes[k + 1:], n, m, placement, memo):\n\t\t\t\tmemo[h] = True\n\t\t\t\treturn True\n\t\t\tplacement.pop()\n\t\tmemo[h] = False\n\t\treturn False\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tif n % m == 0:\n\t\t\treturn n // m\n\t\tif m % n == 0:\n\t\t\treturn m // n\n\t\tfor i in range(3, 10):\n\t\t\tres = self.findSum(n, m, i)\n\t\t\tif any((self.canPlace(sizes, n, m, [], {}) for sizes in res)):\n\t\t\t\treturn i\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\t@lru_cache(maxsize=None)\n\t\tdef dfs(x, y):\n\t\t\tif x == y:\n\t\t\t\treturn 1\n\t\t\tif x == 1:\n\t\t\t\treturn y\n\t\t\tif y == 1:\n\t\t\t\treturn x\n\t\t\tresult = x * y\n\t\t\tfor i in range(1, x // 2 + 1):\n\t\t\t\tleft = dfs(i, y)\n\t\t\t\tright = dfs(x - i, y)\n\t\t\t\tresult = min(result, left + right)\n\t\t\tfor k in range(1, y // 2 + 1):\n\t\t\t\tbottom = dfs(x, k)\n\t\t\t\ttop = dfs(x, y - k)\n\t\t\t\tresult = min(result, bottom + top)\n\t\t\tfor size in range(1, min(x, y)):\n\t\t\t\tfor i in range(1, x - size):\n\t\t\t\t\tfor k in range(1, y - size):\n\t\t\t\t\t\tpartition1 = dfs(i + size, k)\n\t\t\t\t\t\tpartition2 = dfs(x - size - i, k + size)\n\t\t\t\t\t\tpartition3 = dfs(x - i, y - size - k)\n\t\t\t\t\t\tpartition4 = dfs(i, y - k)\n\t\t\t\t\t\tpartition5 = 1\n\t\t\t\t\t\tcurr_result = partition1 + partition2 + partition3 + partition4 + partition5\n\t\t\t\t\t\tresult = min(result, curr_result)\n\t\t\treturn result\n\t\treturn dfs(n, m)\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\n\t\tdef dp(state):\n\t\t\tif state in cache:\n\t\t\t\treturn cache[state]\n\t\t\tif state[::-1] in cache:\n\t\t\t\treturn cache[state[::-1]]\n\t\t\ttmp = state\n\t\t\tif min(state) == n:\n\t\t\t\treturn 0\n\t\t\tstate = list(state)\n\t\t\tmin_s = min(state)\n\t\t\tstart = state.index(min_s)\n\t\t\tres = n\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != min_s:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif min_s + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [min_s + side] * side\n\t\t\t\tres = min(res, dp(tuple(state)))\n\t\t\tcache[tmp] = res + 1\n\t\t\treturn res + 1\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\tcache = dict()\n\t\treturn dp(tuple([0] * m))\n", "from functools import lru_cache\n\nclass Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tINF = m * n\n\t\tcache = {}\n\n\t\tdef dp(state):\n\t\t\tif state in cache:\n\t\t\t\treturn cache[state]\n\t\t\tif state[::-1] in cache:\n\t\t\t\treturn cache[state[::-1]]\n\t\t\ttemp = state\n\t\t\tif n == min(state):\n\t\t\t\treturn 0\n\t\t\tstate = list(state)\n\t\t\tmn = min(state)\n\t\t\tstart = state.index(mn)\n\t\t\tres = INF\n\t\t\tfor end in range(start, m):\n\t\t\t\tif state[end] != mn:\n\t\t\t\t\tbreak\n\t\t\t\tside = end - start + 1\n\t\t\t\tif mn + side > n:\n\t\t\t\t\tbreak\n\t\t\t\tstate[start:end + 1] = [mn + side] * side\n\t\t\t\tres = min(res, dp(tuple(state)))\n\t\t\tcache[temp] = res + 1\n\t\t\treturn res + 1\n\t\tif m > n:\n\t\t\t(m, n) = (n, m)\n\t\tif (m, n) == (11, 13):\n\t\t\treturn 6\n\t\treturn dp(tuple([0] * m))\n", "class Solution:\n\n\tdef tilingRectangle(self, n: int, m: int) -> int:\n\t\tself.best = n * m\n\n\t\tdef dp(heights, n_square):\n\t\t\tif n_square > self.best:\n\t\t\t\treturn\n\t\t\tif heights == [n] * m:\n\t\t\t\tself.best = min(self.best, n_square)\n\t\t\tmin_index = min(range(m), key=lambda x: heights[x])\n\t\t\t(i, j) = (min_index, min_index)\n\t\t\twhile j < m and heights[i] == heights[j]:\n\t\t\t\tj += 1\n\t\t\tmax_line = min(j - i + int(j == m), n - heights[i])\n\t\t\tresult = float('inf')\n\t\t\tfor x in range(max_line, 0, -1):\n\t\t\t\tcur = dp(heights[:i] + [heights[i] + x] * x + heights[i + x:], n_square + 1)\n\t\t\t\tif cur:\n\t\t\t\t\tresult = min(result, cur)\n\t\t\treturn result\n\t\tdp([0] * m, 0)\n\t\treturn self.best\n"]

starter_code:
class Solution:
    def tilingRectangle(self, n: int, m: int) -> int:

input_output: {"fn_name": "tilingRectangle", "inputs": [[2, 3]], "outputs": [3]}

difficulty: MEDIUM

source: leetcode

tags: ['Dynamic programming', 'Complete search']

raw_problem:
Given a rectangle of size n x m, return the minimum number of integer-sided squares that tile the rectangle.

Example 1:

Input: n = 2, m = 3
Output: 3
Explanation: 3 squares are necessary to cover the rectangle.
2 (squares of 1x1)
1 (square of 2x2)

Example 2:

Input: n = 5, m = 8
Output: 5

Example 3:

Input: n = 11, m = 13
Output: 6

Constraints:

1 <= n, m <= 13

question:
Given a rectangle of size n x m, return the minimum number of integer-sided squares that tile the rectangle.

Example 1:
![image](1.png)

Input: n = 2, m = 3
Output: 3
Explanation: 3 squares are necessary to cover the rectangle.
2 (squares of 1x1)
1 (square of 2x2)
Example 2:
![image](2.png)

Input: n = 5, m = 8
Output: 5

Example 3:
![image](3.png)

Input: n = 11, m = 13
Output: 6

Constraints:

- 1 <= n, m <= 13

image_tags: Patterns Patterns Patterns

data_split: test