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:
num=int(input(""))
def check(x,y,z):
    if x==z and x>y:
        print("YES")
        if y==1:
            print(x,y,y)
        else:
            print(x,y,y-1)
    elif x==y==z:
        print("YES")
        print(x,x,x)
    elif x==y and x>z:
        print("YES")
        if z==1:
            print(z,y,z)
        else:
            print(z,y,z-1)
    elif z==y and z>x:
        print("YES")
        if x==1:
            print(x,x,z)
        else:
            print(x,x-1,z)
    else:
        print("NO")

i=0
while i <num:
    x,y,z=(input("").split())
    check(int(x),int(y),int(z))
    i+=1