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 SieveOfEratosthenes(n):
    data=[]
    prime = [True for i in range(n + 1)] 
    p = 2
    while (p * p <= n): 
        if (prime[p] == True): 
            for i in range(p * 2, n + 1, p): 
                prime[i] = False
        p += 1
    prime[0]= False
    prime[1]= False
    for p in range(n + 1): 
        if prime[p]: 
            data.append(p)
    return data
            
# print(len(SieveOfEratosthenes(10**6)))

if __name__=="__main__":
    l = SieveOfEratosthenes(10**6)
    
    for t in range(int(input())):
        data=[]
        n = int(input())
        d=n
        for i in l :
            if i*i>n:
                break
            if n%i==0:
                while n%i==0:
                    data.append(i)
                    n = n/i
        if n>1:
            data.append(n)
            
        a,b,c=data[0],0,0
        if len(data)<=2:
            print("NO")
        else:
            b = data[1]
            if a==data[1]:
                b = data[1]*data[2]
            c = d//(a*b)
            if c==1 or c==b or c==a:
                print("NO")
            else:
                print("YES")
                print(a,b,c)