human
Write me a Python program to find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en given the following:
Given a positive integer n. Find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en.wikipedia.org/wiki/Greatest_common_divisor) of integers x and y.

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^5) — the number of test cases. Description of the test cases follows.

The first and only line of each test case contains a single integer n (10 ≤ n ≤ 10^9).

Output

For each test case, output three distinct positive integers a, b, c satisfying the requirements. If there are multiple solutions, you can print any. We can show that an answer always exists.

Example

Input

6
18
63
73
91
438
122690412

Output

6 9 3
21 39 3
29 43 1
49 35 7
146 219 73
28622 122661788 2

Note

In the first test case, 6 + 9 + 3 = 18 and \operatorname{gcd}(6, 9) = 3.

In the second test case, 21 + 39 + 3 = 63 and \operatorname{gcd}(21, 39) = 3.

In the third test case, 29 + 43 + 1 = 73 and \operatorname{gcd}(29, 43) = 1.
Solve the task in PYTHON3.
assistant
#Here is Python program to find three distinct positive integers a, b, c such that a + b + c = n and \operatorname{gcd}(a, b) = c, where \operatorname{gcd}(x, y) denotes the [greatest common divisor (GCD)](https://en.

def main():
    import sys
    input = sys.stdin.buffer.readline
    import math
    def prime_numbers(x):
        if x < 2:
            return []
        prime_numbers = [i for i in range(x)]
        prime_numbers[1] = 0
        for prime_number in prime_numbers:
            if prime_number > math.sqrt(x):
                break
            if prime_number == 0:
                continue
            for composite_number in range(2 * prime_number, x, prime_number):
                prime_numbers[composite_number] = 0
        return [prime_number for prime_number in prime_numbers if prime_number != 0]
    def soinnsuu(x):
        s = set()
        for i in primes:
            if i > int(math.sqrt(x)):
                break
            elif x % i == 0:
                while x % i == 0:
                    x //= i
                s.add(i)
        if not x == 1:
            s.add(x)
        return s
    from math import gcd
    primes = prime_numbers(50000)
    for _ in range(int(input())):
        n = int(input())
        s = soinnsuu(n - 1)
        for i in primes:
            if i not in s:
                print(n - i - 1, i, 1)
                break
        else:
            print(n)
if __name__ == '__main__':
    main()