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A. GCD vs LCM

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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 of $$$a$$$ and $$$b$$$, and $$$\operatorname{lcm}(c, d)$$$ denotes the least common multiple of $$$c$$$ and $$$d$$$.

Input

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 $$$d$$$.

Output

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

Example

Input

5 4 7 8 9 10

Output

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

Note

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 $$$\gcd(3, 5) = \operatorname{lcm}(1, 1) = 1$$$, $$$3 + 5 + 1 + 1 = 10$$$.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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