B. Little Elephant and Magic Square（数论）

最新推荐文章于 2019-08-20 08:47:59 发布

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最新推荐文章于 2019-08-20 08:47:59 发布

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博客介绍了一种算法，用于解决一个数学问题：当一个3x3的魔方阵中，主对角线的三个元素被遗忘时，如何根据其余元素恢复整个魔方阵。该算法基于魔方阵的性质，即所有行、列和对角线的和相等，通过计算中间元素和对角线元素来完成恢复。

B. Little Elephant and Magic Square

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

Little Elephant loves magic squares very much.

A magic square is a 3 × 3 table, each cell contains some positive integer. At that the sums of integers in all rows, columns and diagonals of the table are equal. The figure below shows the magic square, the sum of integers in all its rows, columns and diagonals equals 15.

The Little Elephant remembered one magic square. He started writing this square on a piece of paper, but as he wrote, he forgot all three elements of the main diagonal of the magic square. Fortunately, the Little Elephant clearly remembered that all elements of the magic square did not exceed 105.

Help the Little Elephant, restore the original magic square, given the Elephant's notes.

Input

The first three lines of the input contain the Little Elephant's notes. The first line contains elements of the first row of the magic square. The second line contains the elements of the second row, the third line is for the third row. The main diagonal elements that have been forgotten by the Elephant are represented by zeroes.

It is guaranteed that the notes contain exactly three zeroes and they are all located on the main diagonal. It is guaranteed that all positive numbers in the table do not exceed 105.

Output

Print three lines, in each line print three integers — the Little Elephant's magic square. If there are multiple magic squares, you are allowed to print any of them. Note that all numbers you print must be positive and not exceed 105.

It is guaranteed that there exists at least one magic square that meets the conditions.

Examples

input

Copy

0 1 1
1 0 1
1 1 0

output

Copy

1 1 1
1 1 1
1 1 1

input

Copy

0 3 6
5 0 5
4 7 0

output

Copy

6 3 6
5 5 5
4 7 4

九宫格中间的数等于任意两面的两个数和的一半，对角线上的元素等于中间的数*3-下方或者右方两个数的和；

#include <iostream>
using namespace std;
int main()
{
    int a[10][10];
        for(int i=0;i<3;i++)
            for(int j=0;j<3;j++)
            cin>>a[i][j];
        a[1][1]=(a[0][1]+a[2][1])/2;
        a[0][0]=3*a[1][1]-(a[0][1]+a[0][2]);
        a[2][2]=3*a[1][1]-(a[0][2]+a[1][2]);
        for(int i=0;i<3;i++)
        {
            for(int j=0;j<2;j++)
            cout<<a[i][j]<<" ";
        cout<<a[i][2]<<endl;
        }
    return 0;
}