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:
def kkk(n):
    for i in range(2,min(1000,n-1)):
        if n%i==0: return i
    return 1

def kkk2(n,p):
    for i in range(p,min(1000000,n-1)):
        if n%i==0: return i
    return 1

for i in range(int(input())):
    n=int(input())
    r=kkk(n)
    if r==1:
        print("NO")
    else:
        n=n//r
        rr=kkk2(n,r+1)
        if rr==1 or rr*rr==n or r==n//rr:
            print("NO")
        else:
            print("YES")
            print(r,rr,n//rr)