CF259B.Little Elephant and Magic Square

普及-

通过率:0%

时间限制:2.00s

内存限制:256MB

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题目描述

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.

小象非常喜欢幻方。

幻方是一个 3×33 \times 3 的表格,每个格子中填有一个正整数,且该表格所有行、列以及两条对角线上的整数之和均相等。下图展示了一个幻方,其所有行、列及对角线上的整数之和均为 1515。

小象曾记住一个幻方,并开始将其写在纸上;但在书写过程中,他忘记了该幻方主对角线上的全部三个元素。幸运的是,小象清楚地记得该幻方中的所有元素均不超过 10510^5。

请根据小象留下的笔记,帮助他恢复原始的幻方。

输入格式

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.

输入的前三行包含小象的笔记。第一行包含幻方第一行的元素,第二行包含第二行的元素,第三行包含第三行的元素。小象遗忘的主对角线元素用 0 表示。

保证笔记中恰好包含三个 0,且它们全部位于主对角线上。同时保证表格中所有正数均不超过 10510^5。

输出格式

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.

输出三行,每行输出三个整数——小象的幻方。如果存在多个幻方,你可以输出其中任意一个。注意:你输出的所有数字必须为正整数,且不能超过 10510^5。

保证至少存在一个满足条件的幻方。

输入输出样例

  • 输入#1

    0 1 1
    1 0 1
    1 1 0

    输出#1

    1 1 1
    1 1 1
    1 1 1
  • 输入#2

    0 3 6
    5 0 5
    4 7 0

    输出#2

    6 3 6
    5 5 5
    4 7 4

输入解题思路,AI测评打分。不知道怎么写?

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