Three matrices Codeforce 393A

                                                                                B. Three matrices

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Chubby Yang is studying linear equations right now. He came up with a nice problem. In the problem you are given ann × n matrix W, consisting of integers, and you should find two n × n matrices A andB, all the following conditions must hold:

• A_ij = A_ji, for alli, j (1 ≤ i, j ≤ n);
• B_ij =  - B_ji, for alli, j (1 ≤ i, j ≤ n);
• W_ij = A_ij + B_ij, for alli, j (1 ≤ i, j ≤ n).

Can you solve the problem?

Input

The first line contains an integer n (1 ≤ n ≤ 170). Each of the followingn lines contains n integers. Thej-th integer in the i-th line is W_ij(0 ≤ |W_ij| < 1717).

Output

The first n lines must contain matrixA. The next n lines must contain matrixB. Print the matrices in the format equal to format of matrixW in input. It is guaranteed that the answer exists. If there are multiple answers, you are allowed to print any of them.

The answer will be considered correct if the absolute or relative error doesn't exceed10^- 4.

Sample test(s)

Input

21 43 2

Output

1.00000000 3.500000003.50000000 2.000000000.00000000 0.50000000-0.50000000 0.00000000

Input

31 2 34 5 67 8 9

Output

1.00000000 3.00000000 5.000000003.00000000 5.00000000 7.000000005.00000000 7.00000000 9.000000000.00000000 -1.00000000 -2.000000001.00000000 0.00000000 -1.000000002.00000000 1.00000000 0.00000000

很水，找规律，可是我竟然花了很长的时间去读题，shit!!!!!!!!!

#include<stdio.h>int main(){int n,i,j;double a[200][200];double temp,b[200][200],c[200][200];scanf("%d",&n);for(i=0;i<n;i++){for(j=0;j<n;j++){scanf("%lf",&a[i][j]);if(i==j)b[i][j]=a[i][j];if(i>j){temp=(a[i][j]+a[j][i])/2.;b[i][j]=b[j][i]=temp;c[i][j]=a[i][j]-temp;c[j][i]=-c[i][j];}}}for(i=0;i<n;i++){for(j=0;j<n;j++){printf("%.8f%s",b[i][j],j==n-1?"\n":" ");}}for(i=0;i<n;i++){for(j=0;j<n;j++){printf("%.8f%s",c[i][j],j==n-1?"\n":" ");}}return 0;}