Problem: 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 

Solution (in PYTHON3):

Solution:
for i in range(int(input())):
    n = int(input())
    ans1 = 1
    ans2 = 1
    ans3 = 1
    p = 2
    while n % p == 0:
        if ans1 == 1:
            ans1 *= p
        elif ans2 == 1 or ans2 == ans1:
            ans2 *= p
        else:
            ans3 *= p
        n //= p
    p = 3
    while p <= n ** 0.5:
        while n % p == 0:
            if ans1 == 1:
                ans1 *= p
            elif ans2 == 1 or ans2 == ans1:
                ans2 *= p
            else:
                ans3 *= p
            n //= p
        p += 2
    if n != 1:
        if ans1 == 1:
            ans1 *= n
        elif ans2 == 1 or ans2 == ans1:
            ans2 *= n
        else:
            ans3 *= n
    if ans1 != 1 and ans2 != 1 and ans3 != 1:
        if ans1 != ans2 and ans1 != ans3 and ans2 != ans3:
            print('YES')
            print(ans1, ans2, ans3)
        else:
            print('NO')
    else:
        print('NO')