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 as mt
def func(n):
    a=[]
    while(n%2==0):
        a.append(2)
        n=n//2
    for i in range(3,mt.ceil(mt.sqrt(n))+1,2):
        #print(i)
        while(n%i==0):
            n=n//i
            a.append(i)
    if(n>2):
        a.append(n)
    return a

t=int(input())
for i in range(t):
    n=int(input())
    C=list(func(n))
    X=[]
    j=C[0]
    X.append(C[0])
    h=1
    k=1
    #print(C)
    while(k<len(C) and h<=j):
        h=h*C[k]
        k+=1
    X.append(h)
    p=1
    if(k>len(C)):
        print("NO")
    else:
        for i in range(k,len(C)):
            p=p*C[i]
        if(p!=1 and p!=X[0] and p!=X[1]):
            X.append(p)
        if(len(set(X))==3):
            print("YES")
            print(*X)
        else:
            print("NO")