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문제

Consider a positive integer X and an N by N matrix A with positive integer entries. Determine the minimum area of a continuous submatrix for which the bitwise or of all its elements equals X.

입력

The standard input contains on the first line integers X and N, separated by a space. On the following N lines there are N positive integers separated by spaces representing a matrix line

출력

The standard output will contain a positive integer representing the minimum area of the submatrix.

제한

  • 2 ≤ N ≤ 500
  • 1 ≤ A[i][j] < 231
  • The bitwise or of two positive integers is the integer whose ith bit equals 0 if and only if the ith bit of both integers is 0.
  • It is guaranteed that for all input data there will always be a solution and the minimum area will be at least 2.

예제 입력 1

11 4
5 9 1 8
7 7 3 1
2 3 1 9
5 5 8 7

예제 출력 1

3