Problem

The determinant of a matrix ,

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is commonly denoted det(A).

A determinant is defined to be

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A determinant can be expanded "by minors" to obtain

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A general determinant for a matrix A has a value

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with no implied summation over j and where (also denoted ) is the cofactor of defined by

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and is the minor of matrix A formed by eliminating row i and column j from A. This process is called determinant expansion by minors (or "Laplacian expansion by minors," sometimes further shortened to simply "Laplacian expansion").

Given a matrix A, the elements of which are all integer numbers, your task is to calculate det(A) modulo 2005.

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Input

The input will contain one or more test cases. The first line of each test case contains one integer n (n <= 100), representing the size of the matrix. The next n lines with n integer numbers each gives the elements of the matrix.
Note that the elements of the matrix are in the range [-32768,32767].

Input will be terminated by a value of 0 for n.

Output

For each matrix A,output exactly one line containing det(A) modulo 2005.

Sample Input

2
1 0
0 1

0

Sample Output

1

Author: Mathematica