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:
#!/usr/bin/env pypy
rr= lambda: input().strip()
rri= lambda: int(rr())
rrm= lambda: [int(x) for x in rr().split()]

def fact(n):
    res=[]
    for i in range(2, int(n**.5)+1):
        if n%i==0:
            res.append(i)
            res.append(n//i)
    if (int(n**.5)**2==n):
        res.pop()
    return res

def sol():
    n=rri()
    f=fact(n)
    #print(f)
    if (len(f)<3):
        print("NO")
        return
    f.sort()
    a=f[0]
    d=n//a
    for i in range(1, len(f)):
        for j in range(i+1, len(f)):
            if f[i]*f[j]==d:
                print("YES")
                print (a, f[i], f[j])
                return
    print("NO")
    return



t=rri()
for _ in range(t):
    #a,b,c=rrm()
    sol()
    #print(ans)