Problem Description

We define e^A as following:

Where A is a n×n symmetric matrix with real elements, I is an identity matrix.
Give you matrix A, your task is to calculate e^A.

Input

There are several test cases;
Each test case begin with a line contains an integer n (1≤n≤100), the following n lines contain n×n symmetric matrix A. The rang of elements of A is (-100,100);
n=0 is the end of input and need not to proceed.

Output

For each test case, output n lines contain matrix e^A , The value of elements of matrix e^A must be accurate up to two decimal places. You may assume the range of elements of e^A is (-10000,10000).

1
2
2
1 0
0 1
0

7.39 
2.72 0.00 
0.00 2.72