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 facts(n):
    l=[]
    for i in range(2,int(pow(n,0.5))+1):
        if n%i==0:
            l.append(i)
            l.append(n//i)
    return list(set(l))
for _ in range(int(input())):
    n=int(input())
    l=facts(n)
    l.sort()
    d={}
    for i in l:
        d[i]=0
    flag = 0
    for i in range(len(l)):
        for j in range(i+1,len(l)):
            a,b=l[i],l[j]
            c=n//(a*b)
            try:
                if d[c]==0 and a!=c and b!=c:
                    print("YES")
                    print(a,b,c)
                    flag = 1
            except:
                continue
            if flag:
                break
        if flag:
            break
    if not flag:
        print("NO")