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.
1
669278611
 10
10
52
91
23
44
99
28
54
99
51

334639303 334639307 1
 4 5 1
25 26 1
43 47 1
9 13 1
21 22 1
47 51 1
13 14 1
26 27 1
47 51 1
23 27 1

# import sys
# from sortedcontainers import SortedSet, SortedDict
# from collections import Counter
from math import gcd

# for line in sys.stdin:
#     numbers = [int(x) for x in line.strip().split()]
#     print(numbers)
#
# for i in range(t):
#     a, m = map(int, input().split())
#     lst = list(map(int, input().split()))

def sol(n):
    # a+b+c=n and gcd(a,b)=n-a-b <= a and <= b
    # a = x*g, b = y*g and g = n - x*g - y*g
    # (x+y+1)*g = n >= 3*g => g <= n/3
    # 2b >= n - a => b >= (n-a)//2
    # for a in range(1, n - 1):
    #     for b in range((n-a)//2, n):
    #         if a == b or a == n - a - b or b == n - a - b or \
    #                 n - a - b < 1 or a % (n-a-b) != 0 or \
    #                 b % (n-a-b) != 0:
    #             continue
    #         if gcd(a, b) == n - a - b:
    #             print(a, b, n-a-b)
    #             return

    for g in range(1, n//3 + 1):
        if n % g != 0:
            continue
        # (x+y+1)*g = n
        for x in range(1, n//g + 1):
            y = n//g - x - 1
            if gcd(x, y) == 1:
                a, b = x*g, y*g
                print(a, b, n - a - b)
                return

if __name__ == "__main__":
    t = int(input())
    for i in range(t):
        n = int(input())
        sol(n)

