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())
for T in range(t):
    n = int(input())
    ans = []

    for i in range(2, int(n ** 0.5) + 1):
        if n % i == 0:
            ans.append(i)
            val = n // i
            for j in range(2, int(val ** 0.5) + 1):
                ans = [i]
                if val % j == 0:
                    ans.append(j)
                    ans.append(val // j)
                    if len(set(ans)) == 3:
                        break
                    
##            print(ans)
            if len(set(ans)) == 3:
                break

            
            ans.append(n // i)
            val = i
            for j in range(2, int(val ** 0.5) + 1):
                if val % j == 0:
                    ans.append(j)
                    ans.append(val // j)
                    if len(set(ans)) == 3:
                        break
                ans = [n // i]
##            print(ans)
            if len(set(ans)) == 3:
                break
        ans = []

    
    if len(ans) == 3:
        print("YES")
        print(*ans)
    else:
        print("NO")