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.

Input

The input contains on the first line integers X and N (2 ≤ N ≤ 500), separated by a space. On the following N lines there are N positive integers separated by spaces representing a matrix line (1 ≤ A[i][j] < 2³¹).

Output

The output will contain a positive integer representing the minimum area of the submatrix. It is guaranteed that for all input data there will always be a solution and the minimum area will be at least 2.

The bitwise or of two positive integers is the integer whose i-th bit equals 0 if and only if the i-th bit of both integers is 0.

Constraints

Time limit: 2 seconds
Memory limit: 128 megabytes

Examples

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

output
3

The submatrix is the highlighted one
(3 | 1 | 9 = 11)

5 9 1 8
7 7 3 1
2 3 1 9
5 5 8 7