Problem: You are given three positive (i.e. strictly greater than zero) integers x, y and z.

Your task is to find positive integers a, b and c such that x = max(a, b), y = max(a, c) and z = max(b, c), or determine that it is impossible to find such a, b and c.

You have to answer t independent test cases. Print required a, b and c in any (arbitrary) order.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 2 ⋅ 10^4) — the number of test cases. Then t test cases follow.

The only line of the test case contains three integers x, y, and z (1 ≤ x, y, z ≤ 10^9).

Output

For each test case, print the answer:

  * "NO" in the only line of the output if a solution doesn't exist; 
  * or "YES" in the first line and any valid triple of positive integers a, b and c (1 ≤ a, b, c ≤ 10^9) in the second line. You can print a, b and c in any order. 

Example

Input


5
3 2 3
100 100 100
50 49 49
10 30 20
1 1000000000 1000000000


Output


YES
3 2 1
YES
100 100 100
NO
NO
YES
1 1 1000000000

Solution (in PYTHON3):

Solution:
def Max(x,y,z):
    a,b,c=-1,-1,-1
    if(x==y==z):
        a,b,c=x,x,x
    elif(x==y and max(y,z)==y):
        a=z
        b=x
        c=z
    elif(x==y and max(y,z)==z):

        a=-1
        b=-1
        c=-1

    elif(  max(x,y)==x and y==z):

        a = -1
        b = -1
        c = -1
    elif(max(x,y)==y and y==z):
        a=x
        b=x
        c=y
    elif(x==z and max(y,z)==z):
        a=x
        b=y
        if(y==1):
            c=y
        else:
            c=y-1
    elif(x==z and max(y,z)==y):
        a,b,c=-1,-1,-1
    return(a,b,c)
n=int(input())
for i in range(0,n):
    x,y,z=map(int,input().split())
    a,b,c=Max(x,y,z)
    if(a==-1):
        print("NO")
    else:
        print("YES")
        print(str(a)+" "+str(b)+" "+str(c))