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:
import math
for _ in range(int(input())):
    n = int(input())
    f = []
    i = 2
    while i <= math.sqrt(n):
        if n % i == 0:
            if n // i == 0:
                f.append(i)
            else:
                f.append(n//i)
                f.append(i)
        i = i + 1
    f = set(f)
    f = list(f)
    #print(f)
    ln = len(f)
    f.sort()
    f1 = 0
    for i in range(ln):
        for j in range(1,ln):
            for k in range(2,ln):
                if f[i]*f[j]*f[k] == n:
                    print("YES")
                    print(f[i],f[j],f[k])
                    f1 = 1
                    break
            if f1 == 1:
                break
        if f1 == 1:
            break
    if f1 == 0:
        print("NO")