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 sys
input=sys.stdin.readline

t=int(input())
for i in range(t):
    x=int(input())
    ar=[]
    l=0
    a=1
    b=1
    c=1
    ct=0
    bl=False
    for j in range(2,int(x**(0.5))):
        if(x%j==0 and ct==0):
            a=j
            ct+=1
        elif(x%j==0 and ct==1):
            temp=j
            if(x%(a*temp)==0 and x//(a*temp)!=a and x//(a*temp)!=temp):
                b=temp
                c=x//(a*temp)
                bl=True
                break
            
    if(bl==True):
        print("YES")
        print(a,b,c)
    else:
        print("NO")