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10205_AllLatinSquares

2022-5-16 18:16| 发布者: Hocassian| 查看: 103| 评论: 0|原作者: 肇庆学院ACM合集

摘要:

C:\Users\Administrator\Downloads\2019-10-12-10-14-3-89504659476699-Problem List-采集的数据-后羿采集器.html

Pro.ID

10205

Title

All Latin Squares

Title链接

http://10.20.2.8/oj/exercise/problem?problem_id=10205

AC

Submit

Ratio

50.00%

时间&空间限制

Time Limit: 1000/500 MS (Java/Others) Memory Limit: 65536/65536 K (Java/Others)

描述

A square arrangement of numbers

1 2 3 4 5
2 1 4 5 3
3 4 5 1 2
4 5 2 3 1
5 3 1 2 4

is a 5 × 5 Latin Square because each whole number from 1 to 5 appears once and only once in each row and column.

Write a program that will compute the number of N × N Latin Squares whose first row is:

1 2 3 4 5.......N

Your program should work for any N from 2 to 7.

输入

One line containing the integer N.

输出

Description

A square arrangement of numbers

1 2 3 4 5
2 1 4 5 3
3 4 5 1 2
4 5 2 3 1
5 3 1 2 4

is a 5 × 5 Latin Square because each whole number from 1 to 5 appears once and only once in each row and column.

Write a program that will compute the number of N × N Latin Squares whose first row is:

1 2 3 4 5.......N

Your program should work for any N from 2 to 7.

Input

One line containing the integer N.

Output

A single integer telling the number of latin squares whose first row is 1 2 3 ... N.

Sample Input

Sample Output

1344

Source

USACO training course

样例输入

样例输出