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 pf(n):
    l =[]
    while n % 2 == 0: 
        l.append(2) 
        n = n / 2
    for i in range(3,int(math.sqrt(n))+1,2): 
        while n % i== 0: 
            l.append(i) 
            n = n / i 
    if n > 2: 
        l.append(n)
    return l
for _ in range(input()):
    n = input()
    a = pf(n)
     
    if len(a)<3:
        print "NO"
    elif len(set(a))<3:
        b = list(set(a))
        for i in range(len(b)):
            b[i] = [b[i],a.count(b[i])]
        b.sort(key = lambda x: x[1])
        lil = n
        if len(b)==1 and b[0][1]<6:
            print "NO"
        elif len(b)==1 and b[0][1]>5:
            print "YES"
            l = 1
            for i in range(len(a)-3):
                j = i+3
                l *= a[i]
            print a[0], a[1]*a[2], l
        elif len(b)==2 and b[1][1]==2 and b[0][1]==1:
            print "NO"
        else:
            print "YES"
            print b[0][0], b[1][0], lil/(b[0][0]* b[1][0])
    else:
        print "YES"
        b = list(set(a))
        print b[0],b[1],n/(b[0]*b[1])