Determinant

The matrix of size n×n is given. Find its determinant.

Input

The first line contains the number n (n ≤ 100). Each of the next n lines contains n integers not greater than 1000000 by absolute value. The j-th number in the (i+1)-th line gives the j-th element of i-th row in the matrix.

Output

Print the value of determinant.

Examples