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:
t = int(input())
while t:
    t-=1
    n = int(input())
    factors = []
    for i in range(2,int(n**0.5)+1):
        if n%i==0:
            factors.append(i)
            if n//i!=i:
                factors.append(n//i)
    if len(factors)<2:
        print("NO")
        continue
    factors.sort()
    done = False 
    for i in range(len(factors)):
        for j in range(i+1,len(factors)):
            a = factors[i]
            b = factors[j]
            c = n//(a)
            if c%b!=0:
                continue 
            c = c//b
            if c>=2 and a!=c and b!=c :
                done = True
                print("YES")
                print(a,b,c)
                break 
        if done:
            break 
    if not done:
        print("NO")