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 collections,math
for _ in range(int(input())):
    n=int(input())
    factors=[]
    flag=False
    d=collections.defaultdict(int)
    for i in range(2,int(math.sqrt(n))+1):
        if n%i==0:
            d[i]=1
            factors.append(i)
            if (n//i) !=  i:
                d[n//i]=1
                factors.append(n//i)
    factors.sort()
    for i in range(len(factors)-1):
        for j in range(i+1,len(factors)):
            k=n//(factors[i]*factors[j])
            if d[k]==1 and factors[i]*factors[j]*k==n and factors[i]!=k and factors[j]!=k:
                flag=True
                print('YES')
                print(factors[i],factors[j],k)
                break
        if flag:
            break
    if not flag:
        print('NO')