""" Fraises dans une boîte(6) 想定解 6乗ver """ import sys from sys import stdin H,W = map(int,stdin.readline().split()) S = [list(map(int,stdin.readline().split())) for i in range(H)] # 制約チェック assert 1 <= H <= 22 assert 1 <= W <= 22 assert len(S) == H for s in S: assert len(s) == W for i in s: assert i == 0 or i == 1 # 領域の和を高速に導出するための2次元累積和 SSum = [[0] * (W+1) for i in range(H+1)] for i in range(H): for j in range(W): SSum[i+1][j+1] += S[i][j] for i in range(H): for j in range(W+1): SSum[i+1][j] += SSum[i][j] for i in range(H+1): for j in range(W): SSum[i][j+1] += SSum[i][j] # メモ化用の4次元list inf = float("inf") lis = [[[[0] * (W+1) for i in range(W+1)] for j in range(H+1)] for k in range(H+1)] # ここからdp for hsize in range(1,H+1): #縦のサイズが小さい領域から調べる for wsize in range(1,W+1): #横のサイズが小さい領域から調べる for x1 in range(H): #左上のx座標 x2 = x1 + hsize if x2 > H: break for y1 in range(W): #左上のy座標 y2 = y1 + wsize if y2 > W: break # ここから、最小値の導出処理 now_ans = inf # 左上領域の空行カウント用の配列 zerox = [0] zeroy = [0] for tmpx in range(x1,x2): nsum = 0 for tmpy in range(y1,y2): nsum += S[tmpx][tmpy] if nsum == 0: pl = 1 else: pl = 0 zerox.append(zerox[-1] + pl) for tmpy in range(y1,y2): nsum = 0 for tmpx in range(x1,x2): nsum += S[tmpx][tmpy] if nsum == 0: pl = 1 else: pl = 0 zeroy.append(zeroy[-1] + pl) #print (zerox,zeroy) for xmid in range(x1,x2+1): for ymid in range(y1,y2+1): #右下が0で無い場合、駄目 if SSum[x2][y2] - SSum[xmid][y2] - SSum[x2][ymid] + SSum[xmid][ymid] != 0: continue #左上・右下共に0の場合は推移の意味が無いのでダメ if (xmid-x1) * (ymid-y1) == 0 and (x2-xmid) * (y2-ymid) == 0: continue cost = 0 # 左上区間の1の個数 lu1 = SSum[xmid][ymid] - SSum[xmid][y1] - SSum[x1][ymid] + SSum[x1][y1] cost += (xmid-x1-zerox[xmid-x1]) * (ymid-y1-zeroy[ymid-y1]) - lu1 # 左下と右上 cost += lis[xmid][x2][y1][ymid] + lis[x1][xmid][ymid][y2] # デバッグ用 #print (x1,xmid,x2,y1,ymid,y2,cost) now_ans = min(now_ans , cost) lis[x1][x2][y1][y2] = now_ans # デバッグ用 #print (x1,x2,y1,y2,now_ans) print (lis[0][H][0][W])