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 primes(n):
        while n % 2 == 0:
            prime.append(2)
            n = n / 2
        for i in range(3, int(math.sqrt(n)) + 1, 2):
            while n % i == 0:
                prime.append(i)
                n = n / i
        if n > 2:
            prime.append(int(n))

t=int(input())
for _ in range(t):
    n=int(input())
    prime=[]
    primes(n)
    p={}
    for i in prime:
        if i in p.keys():
            p[i]+=1
        else:
            p[i]=1
    g=list(p.keys())
    if len(g)==1:
        if p[g[0]]>=6:
            print("YES")
            p1=p[g[0]]-2
            print(g[0],g[0]**2,g[0]**(p[g[0]]-3))
        else:
            print("NO")
        continue
    if len(g)==2:
        if p[g[0]]+p[g[1]]>3:
            print("YES")
            n1 = g[0]
            n2 = g[1]
            p1 = p[g[0]]
            p2 = p[g[1]]
            print(n1, n2, (pow(n1, p1 - 1) * pow(n2, p2 - 1)))
        else:
            print("NO")

    else:
        print("YES")
        ans=pow(g[0],p[g[0]]-1)*pow(g[1],p[g[1]]-1)
        for i in range(2,len(g)):
            ans*=pow(g[i],p[g[i]])
        print(g[0],g[1],ans)