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())
    f = []
    for j in range(2, int(n**(1/2))):
        while n % j == 0:
            f.append(j)
            n = int(n/j)
    if n > 1:
        f.append(n)
    if len(f) >= 3:
        if len(f) == 3:
            if f[0] != f[1] and f[1] != f[2] and f[2] != f[0]:
                print('YES')
                print(f[0],f[1],f[2])
            else:
                print('NO')
        else:
            f0 = f[0]
            f1 = 1
            f2 = 1
            if f[1] == f[0]:
                f1 = f[1] * f[2]
                for j in range(3, len(f)):
                    f2 *= f[j]
            else:
                f1 = f[1]
                for j in range(2, len(f)):
                    f2 *= f[j]
            if f0 != f1 and f1 != f2 and f2 != f0:
                print('YES')
                print(f0, int(f1), int(f2))
            else:
                print('NO')

    else:
        print('NO')