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:
from itertools import permutations, combinations
loop = int(input())
while loop != 0:
    loop -= 1
    x, y, z = input().split()
    x, y, z = int(x), int(y), int(z)
    check = True
    answer = ""
    temp = [x, y, z]
    a = max(temp)
    if (x == a and y == a) or (x == a and z == a) or (y == a and z == a):
        answer += str(a) + " "
    else:
        check = False
    b = min(temp)

    if check == True:
        print("YES\n" + answer + " " +str(b) + " " + str(b))
    else:
        print("NO")