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 prime(n):
    if n<3:
        return not n&1

    res=True
    i=2
    while i*i<=n:
        if n%i==0:
            res=False
            break
        i+=1

    return res

def sieve(n):
    num=[ True ]*(n+1)
    i=2
    primes=[]
    while i*i<n+1:
        if num[i]:
            j=i*i
            while j<=n:
                num[j]=False
                j+=i
        i+=1

    for i in range(2,n+1):
        if num[i]:
            primes.append(i)

    return primes

primes=sieve(10**6)

def factor(n,i=0):
    if n==1:
        return " "

    if prime(n):
        return str(n)+":"+"1"+"  "

    while primes[i]<=n:
        if n%primes[i]==0:
            l=0
            while n%primes[i]==0:
                n//=primes[i]
                l+=1
            return str(primes[i])+":"+str(l)+" "+factor(n,i+1)

        i+=1

def main():
    for _ in range(int(input())):
        n=int(input())
        s=factor(n)
        s=s.split(" ")
        s.pop(-1)
        s.pop(-1)
        s=[list(map(int,e.split(":"))) for e in s]
        a=s[0][0]
        s[0][1]-=1
        if s[0][1]>=2:
            b=s[0][0]**2
            s[0][1]-=2
            c=n//(a*b)
        else:
            try:
                b=(s[0][0]**s[0][1])*s[1][0]
                s[1][1]-=1
                c=n//(a*b)
            except:
                b=s[0][0]**s[0][1]
                c=1

        res= a>1 and b>1 and c>1 and a!=b and b!=c and a!=c
        if res:
            print("YES")
            print(a,b,c)
        else:
            print("NO")

main()