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 PYTHON):

Solution:
import math

def primeFactors(n):
    ar = []
    while n % 2 == 0: 
        ar.append(2)
        n = n / 2
          
    for i in range(3, int(math.sqrt(n))+1, 2): 
          while n % i == 0: 
            ar.append(i)
            n = n / i 
              
    if n > 2: 
        ar.append(n)

    return ar

for _ in xrange(input()):
    n = input()
    ar = primeFactors(n)
    ar.sort()
    ans = []
    if len(ar) < 3:
        print "NO"
        continue
    ans.append(ar.pop(0))
    if ar[0] in ans:
        ans.append(ar[0]*ar[1])
        ar = ar[2:]
        if len(ar) == 0:
            print "NO"
        else:
            pr = 1
            for x in ar:
                pr = pr*x
            if pr in ans:
                print "NO"
            else:
                print "YES"
                ans.append(pr)
                print " ".join(str(x) for x in ans)
    else:
        ans.append(ar.pop(0))
        if len(ar) == 0:
            print "NO"
        else:
            pr = 1
            for x in ar:
                pr = pr*x
            if pr in ans:
                print "NO"
            else:
                print "YES"
                ans.append(pr)
                print " ".join(str(x) for x in ans)