Three Pairwise Maximums
Description
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.
The first line of the input contains one integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. Then $t$ test cases follow.
The only line of the test case contains three integers $x$, $y$, and $z$ ($1 \le x, y, z \le 10^9$).
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 $c$ ($1 \le a, b, c \le 10^9$) in the second line. You can print $a$, $b$ and $c$ in any order.
Input
The first line of the input contains one integer $t$ ($1 \le t \le 2 \cdot 10^4$) — the number of test cases. Then $t$ test cases follow.
The only line of the test case contains three integers $x$, $y$, and $z$ ($1 \le x, y, z \le 10^9$).
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 $c$ ($1 \le a, b, c \le 10^9$) in the second line. You can print $a$, $b$ and $c$ in any order.
Samples
5
3 2 3
100 100 100
50 49 49
10 30 20
1 1000000000 1000000000
YES
3 2 1
YES
100 100 100
NO
NO
YES
1 1 1000000000