{"raw_statement":[{"iden":"problem statement","content":"You are given a matrix $A$ with $H$ rows and $W$ columns. The value of each of its elements is $0$ or $1$. For an integer pair $(i, j)$ such that $1 \\leq i \\leq H$ and $1 \\leq j \\leq W$, we denote by $A_{i,j}$ the element at the $i$\\-th row and $j$\\-th column.\nYou can perform the following operation on the matrix $A$ any number of times (possibly zero):\n\n*   Choose an integer $i$ such that $1 \\leq i \\leq H$. For every integer $j$ such that $1 \\leq j \\leq W$, replace the value of $A_{i,j}$ with $1-A_{i,j}$.\n\n$A_{i,j}$ is said to be **isolated** if and only if there is no adjacent element with the same value; in other words, if and only if none of the four integer pairs $(x,y) = (i-1,j),(i+1,j),(i,j-1),(i,j+1)$ satisfies $1 \\leq x \\leq H, 1 \\leq y \\leq W$, and $A_{i,j} = A_{x,y}$.\nDetermine if you can make the matrix $A$ in such a state that no element is isolated by repeating the operation. If it is possible, find the minimum number of operations required to do so."},{"iden":"constraints","content":"*   $2 \\leq H,W \\leq 1000$\n*   $A_{i,j} = 0$ or $A_{i,j} = 1$\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$H$ $W$\n$A_{1,1}$ $A_{1,2}$ $\\ldots$ $A_{1,W}$\n$A_{2,1}$ $A_{2,2}$ $\\ldots$ $A_{2,W}$ \n$\\vdots$\n$A_{H,1}$ $A_{H,2}$ $\\ldots$ $A_{H,W}$"},{"iden":"sample input 1","content":"3 3\n1 1 0\n1 0 1\n1 0 0"},{"iden":"sample output 1","content":"1\n\nAn operation with $i = 1$ makes $A = ((0,0,1),(1,0,1),(1,0,0))$, where there is no longer an isolated element."},{"iden":"sample input 2","content":"4 4\n1 0 0 0\n0 1 1 1\n0 0 1 0\n1 1 0 1"},{"iden":"sample output 2","content":"2"},{"iden":"sample input 3","content":"2 3\n0 1 0\n0 1 1"},{"iden":"sample output 3","content":"\\-1"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}