You are given a rectangular matrix of size n x m consisting of integers from 1 to 2 cdot 10^5 . In one move, you can: A cyclic shift is an operation such that you choose some j ( 1 <= j <= m ) and set a_{1, j} := a_{2, j}, a_{2, j} := a_{3, j}, ... , a_{n, j} := a_{1, j} simultaneously. You want to perform the minimum number of moves to make this matrix look like this: In other words, the goal is to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, ... , a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, ... , a_{n, m} = n cdot m (i.e. a_{i, j} = (i - 1) cdot m + j ) with the minimum number of moves performed. The first line of the input contains two integers n and m ( 1 <= n, m <= 2 cdot 10^5, n cdot m <= 2 cdot 10^5 ) -- the size of the matrix. The next n lines contain m integers each. The number at the line i and position j is a_{i, j} ( 1 <= a_{i, j} <= 2 cdot 10^5 ). Print one integer -- the minimum number of moves required to obtain the matrix, where a_{1, 1} = 1, a_{1, 2} = 2, ... , a_{1, m} = m, a_{2, 1} = m + 1, a_{2, 2} = m + 2, ... , a_{n, m} = n cdot m ( a_{i, j} = (i - 1)m + j ). In the first example, you can set a_{1, 1} := 7, a_{1, 2} := 8 and a_{1, 3} := 9 then shift the first, the second and the third columns cyclically, so the answer is 6 . It can be shown that you cannot achieve a better answer. In the second example, the matrix is already good so the answer is 0 . In the third example, it is enough to shift the second column cyclically twice to obtain a good matrix, so the answer is 2 .