human
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.

Can you provide 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?
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.

import sys
tokens = ''.join(sys.stdin.readlines()).split()[::-1]

def next(): return tokens.pop()
def nextInt(): return int(next())
def nextFloat(): return float(next())
def getIntArray(n): return [nextInt() for _ in range(n)]
def getFloatArray(n): return [nextFloat() for _ in range(n)]
def getStringArray(n): return [next() for _ in range(n)]

testcase = True
def solve(testcase = 1):
    def gcd(a, b): return a if b == 0 else gcd(b, a % b)

    N = nextInt()
    if N & 1:
        i = 1
        while i * 2 < N:
            for z in range(1, 10):
                j = N - i - z
                if i != j and j != z and z != i and gcd(i, j) == z:
                    print(i, j, z)
                    return
            i += 1
        7 / 0
    else:
        print(N - 1 >> 1, N >> 1, 1)
    pass

if testcase is None:
    testcaseCount = 1
    while tokens:
        solve(testcaseCount)
        testcaseCount += 1
else:
    testcaseCount = nextInt() if testcase else 1
    for tc in range(testcaseCount):
        solve(tc + 1)
    assert not tokens