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
def printDivisors(n) : 
    i = 1
    l=[]
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n / i == i) : 
                l.append(i) 
            else : 
                l.append(i)
                l.append(n//i)
        i = i + 1
    return l
t=int(input())
for _ in range(t):
    n=int(input())
    a=printDivisors(n)
    a.sort()
    #print(a)
    z=-1
    d={}
    d[a[0]]=1
    l=[]
    c=0
    for i in range(1,len(a)):
        for j in range(i+1,len(a)):
            if n%(a[i]*a[j])==0:
                if (n//(a[i]*a[j])) in d and (a[i]>=2 and a[j]>=2 and (n//(a[i]*a[j]))>=2):
                    print("YES")
                    z=0
                    l.append(a[i])
                    l.append(a[j])
                    l.append((n//(a[i]*a[j])))
                    l.sort()
                    print(*l)
            if z==0:
                c=1
                break
        if c==1:
            break

        d[a[i]]=1
    if z==-1:
        print("NO")