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:
for _ in range(int(input())):
    n=int(input())
    m=n
    l=[]
    t=1
    f=0
    g=0
    if n<8:
        print("NO")
        
    else:
        for i in range(2,int(n**0.5)+1):
            if n%i==0:
                if not l:
                    l.append(i)
                    f=1
                    break
#         print(l)
        if f==1:
            n=n//l[-1]
            for i in range(l[-1],int(n**0.5)+1):
                while n%i==0:
                    if l[-1]==t*i:
                        t=t*i
                    else:
                        l.append(t*i)
#                         print(l)
                        n=n//i
                        g=1
                        break
                
                    n=n//i
                if g==1:
                    break
            if len(l)<2:
#                 print(l)
                if t==1 or t==l[-1]:
                    print("NO")
                else:
                    l.append(t)
                    m=m//(l[0]*l[1])
#                     print(l)
                    if m>=2:
                        l.append(m)
            
                    s=set(l)
                    if len(s)<len(l) or len(l)<=2:
                        print("NO")
                    else:
                        print("YES")
                        print(" ".join(map(str,l)))
            else:
                m=m//(l[0]*l[1])
                if m>=2:
                    l.append(m)
#                 print(l)
                s=set(l)
                if len(s)<len(l) or len(l)<=2:
                    print("NO")
                else:
                    print("YES")
                    print(" ".join(map(str,l)))
        else:
            print("NO")