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 T in range(int(input())):
    N = int(input())
    D = set()
    for I in range(2, int(N**0.5)+1):
        if N % I == 0:
            D.add(I)
            D.add(N//I)
    D = sorted(list(D))
    F = 0
    if len(D) < 3:
        F = 1
        print('NO')
    else:
        for I in range(len(D)):
            for J in range(len(D)):
                if I != J:
                    X = N/(D[I]*D[J])
                    if X != D[I] and X != D[J] and X > 1 and X % 1 ==0:
                        F = 1
                        print('YES')
                        print(D[I], D[J], int(X))
                        break
            if F == 1:
                break
    if F == 0:
        print('NO')