B'Misha has a square n x n matrix, where the number in row i and column j is equal to a_{i, j} . Misha wants to modify the matrix to contain exactly k distinct integers. To achieve this goal, Misha can perform the following operation zero or more times: Please find the minimum number of operations that Misha needs to achieve his goal. The first input line contains two integers n and k ( 1 <= q n <= q 500, 1 <= q k <= q n^2 ) -- the size of the matrix and the desired amount of distinct elements in the matrix. Then n lines follows. The i -th of them contains n integers a_{i, 1}, a_{i, 2}, ldots, a_{i, n} ( 1 <= q a_{i,j} <= q n^2 ) -- the elements of the i -th row of the matrix. Output one integer -- the minimum number of operations required. In the first test case the answer is 1 , because one can change the value in the bottom right corner of the matrix to 1 . The resulting matrix can be found below: In the second test case the answer is 2 . First, one can change the entire matrix to contain only 1 s, and the change the value of any single cell to 2 . One of the possible resulting matrices is displayed below: '...