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 pr(a,m):
    n=len(a)
    d={}
    l=[]
    for i in range(n):
        d[a[i]]=i
    c=0
    for i in range(n-1):
        for j in range(i+1,n):
            if ((a[i]*a[j]<=m) and (a[i]*a[j]!=0) and (m%(a[i]*a[j])==0)):
                check=m//(a[i]*a[j])
                if( check!=1 and check!=a[i] and check!=a[j] and check in d and d[check]>i and d[check]>j):
                    l=[a[i],a[j],check]
                    return l
    
def p(n) : 
    l=[]
    i = 1
    while i <= math.sqrt(n): 
        if (n % i == 0) : 
            if (n / i == i) :
                if(i!=1):
                    l.append(i)
            else : 
                if(i!=1):
                    l.append(i)
                if(n//i!=1):
                    l.append(n//i) 
        i = i + 1
    return l    
for _ in range(int(input())):
    x=int(input())
    l=p(x)
    l.sort()
    #print(l,"d")
    aa=pr(l,x)
    if(aa==None):
        print("NO")
    else:
        print("YES")
        aa.sort()
        print(*aa)
    #print(aa)