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
t=int(input())
for i in range(t):
    f=False
    a=-1
    b=-1
    c=-1
    n=int(input())
    primes=set()
    st=math.ceil(n**0.5)+1
    p=[True]*(st)
    for i in range(2,st):
        if p[i]:
            primes.add(i)
            for j in range(i,st,i):
                p[j]=False
    #print(primes)
    for i in range(2,st):
        if f:
            break
        if n%i==0:
            a=i
            bc=n//i
            st1=math.ceil(bc**0.5)+1
            if bc not in primes:
                for j in range(2,st1):
                    if j==a:
                        continue
                    if bc%j==0 :
                        if bc//j==a or j==bc//j:
                            continue
                        b=j
                        c=bc//j
                        f=True
                        #print(a,b,c)
                        break
    if f:
        print("YES")
        print(a,b,c)
    else:
        print("NO")
#print(15*3*4115)