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:
d=dict()
import math
def primeFactors(n):
    c=0
    while n % 2 == 0:
        c+=1
        n = n // 2
    if c!=0:
        d[2]=c
    for i in range(3, int(math.sqrt(n)) + 1, 2):
        c=0
        while n % i == 0:
            c+=1
            n = n // i
        if c!=0:
            d[i]=c
    if n > 2:
        if n in d:
            d[n]+=1
        else:
            d[n]=1
I=input
for _ in range(int(I())):
    d.clear()
    n=int(I())
    primeFactors(n)
    # print(d)
    k=list(d.keys())
    v=list(d.values())
    if len(set(d))==1:
        if v[0]>=6:
            print('YES')
            a=k[0]
            b=k[0]**2
            c=k[0]**(v[0]-3)
            print(a,b,c)
        else:
            print('NO')

    elif len(set(d))==2:
        if sum(v)>=4:
            print('YES')
            a=k[0]
            b=(k[0]**(v[0]-1))*(k[1]**(v[1]-1))
            c=k[1]
            print(a,b,c)
        else:
            print('NO')
    else:
        a=k[0]**v[0]
        b=k[1]**v[1]
        c=1
        for i in range(2,len(k)):
            c*=(k[i]**v[i])
        print('YES')
        print(a,b,c)