You are given one integer number n. Find three distinct integers a, b, c such that 2 ≤ a, b, c and a ⋅ b ⋅ c = n or say that it is impossible to do it.

If there are several answers, you can print any.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 100) — the number of test cases.

The next n lines describe test cases. The i-th test case is given on a new line as one integer n (2 ≤ n ≤ 10^9).

Output

For each test case, print the answer on it. Print "NO" if it is impossible to represent n as a ⋅ b ⋅ c for some distinct integers a, b, c such that 2 ≤ a, b, c.

Otherwise, print "YES" and any possible such representation.

Example

Input


5
64
32
97
2
12345


Output


YES
2 4 8 
NO
NO
NO
YES
3 5 823 
#!/usr/bin/env python3

R = lambda: list(map(int, input().split()))


def solve():
    n = R()[0]
    a, cnt, i = [0, 0], 0, 2
    while i * i < n and cnt < 2:
        if n % i == 0:
            a[cnt] = i
            cnt += 1
            n //= i
        i += 1
    if cnt < 2:
        print("NO")
    else:
        print("YES\n", a[0], a[1], n)


o_o = R()[0]
for _ in range(o_o):
    solve()
