GCD vs LCM

题意翻译

本题有多测。 给定一个正整数 $n$，求一组正整数 $a$, $b$, $c$, $d$，使得 $a+b+c+d=n$，并且 $\gcd(a,b) = \operatorname{lcm}(c,d)$。本题有 SPJ，求出任意一组即可。 **输入格式** 第一行一个正整数 $t$，表示测试数据组数，接下来 $t$ 行，每行一个正整数 $n$。 **输出格式** 对于每组数据，输出任意一组 $a$, $b$, $c$, $d$。数据保证一定有解。 **说明/提示** $4\le n\le 10^9$ $1\le t\le 10^4$

题目描述

You are given a positive integer $ n $ . You have to find $ 4 $ positive integers $ a, b, c, d $ such that - $ a + b + c + d = n $ , and - $ \gcd(a, b) = \operatorname{lcm}(c, d) $ . If there are several possible answers you can output any of them. It is possible to show that the answer always exists. In this problem $ \gcd(a, b) $ denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of $ a $ and $ b $ , and $ \operatorname{lcm}(c, d) $ denotes the [least common multiple](https://en.wikipedia.org/wiki/Least_common_multiple) of $ c $ and $ d $ .

输入输出格式

输入格式

The input consists of multiple test cases. The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Description of the test cases follows. Each test case contains a single line with integer $ n $ ( $ 4 \le n \le 10^9 $ ) — the sum of $ a $ , $ b $ , $ c $ , and $ d $ .

输出格式

For each test case output $ 4 $ positive integers $ a $ , $ b $ , $ c $ , $ d $ such that $ a + b + c + d = n $ and $ \gcd(a, b) = \operatorname{lcm}(c, d) $ .

输入输出样例

输入样例 #1

5
4
7
8
9
10

输出样例 #1

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

说明

In the first test case $ \gcd(1, 1) = \operatorname{lcm}(1, 1) = 1 $ , $ 1 + 1 + 1 + 1 = 4 $ . In the second test case $ \gcd(2, 2) = \operatorname{lcm}(2, 1) = 2 $ , $ 2 + 2 + 2 + 1 = 7 $ . In the third test case $ \gcd(2, 2) = \operatorname{lcm}(2, 2) = 2 $ , $ 2 + 2 + 2 + 2 = 8 $ . In the fourth test case $ \gcd(2, 4) = \operatorname{lcm}(2, 1) = 2 $ , $ 2 + 4 + 2 + 1 = 9 $ . In the fifth test case $ \gcd(3, 5) = \operatorname{lcm}(1, 1) = 1 $ , $ 3 + 5 + 1 + 1 = 10 $ .