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 getFactors(n):
    fact = []
    i =2
    while i*i <=n:
        if n%i==0:
            fact.append(i)
            if(i!=n//i):
                fact.append(n//i)
        i+=1
    return fact

t = int(input())
while t>0:
    n = int(input())
    fact = getFactors(n)
    fact.sort()
    found = False
    for i in range(len(fact)-1):
        for j in range(len(fact)):
            a = fact[i]
            b = fact[j]
            c = n//(a*b)
            if c in fact:
                if a-b!=0 and b-c!=0 and a-c!=0:
                    print("YES")
                    print(a,b,c)
                    found = True
                    break
        if found:
            break
    if not found:
        print("NO")
    t-=1