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
# sys.stdin=open("input1.in","r")
# sys.stdout=open("outpul.out","w")
for _ in range(int(input())):
    N=int(input())
    Factors=[]
    FLAG=0
    for i in range(2,int(pow(N,0.5))+1):
        if N%i==0:
            X=i
            Z=N//i
            for j in range(2,int(pow(Z,0.5))+1):
                if Z%j==0:
                    X1=Z//j
                    if X1!=j and X1!=X and j!=X:
                        print("YES")
                        print(X1,j,X)
                        FLAG=1
                        break
            if FLAG==1:
                break
    if FLAG==0:
        print("NO")