BIGZHUGOD and His Friends II

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem Description

BIGZHUGOD and his three friends are playing a game in a triangle ground.

The number of BIGZHUGOD is 0, and his three friends are numbered from 1 to 3. Before the game begins, three friends stand on three vertices of triangle in numerical order (1 on A, 2 on B, 3 on C), BIGZHUGOD stands inside of triangle.

Then the game begins, three friends run to the next vertex in uniform speed and in straight direction (1 to B, 2 to C, 3 to A and there speeds may different). And BIGZHUGOD can stand in any position inside the triangle.

When any of his friends arrives at next vertex, the game ends.

BIGZHUGOD and his friends have made an agreement: we assume that the beginning is time 0, if during the game, you can find a moment that BIGZHUGOD can block the sight line of 1 to C, 2 to A, 3 to B. Then each friend has to treat BIGZHUGOD with a big meal.

Now BIGZHUGOD knows the lengths of time that his three friends need run to next vertices t1, t2 and t3. He wants to know whether he has a chance to gain three big meals, of course he wants to know in which exciting moment t, he can block three friends\' sight line.

Input

The first line contains an integer T, indicating the number of test cases (T ≤ 1000).

For each case there are three integer t1, t2, t3 (1 ≤ t1, t2, t3 ≤ 100).

Output

If BIGZHUGOD has a chance to gain big meal from his friends, output "YES" and the exciting moment t rounding to 4 digits after decimal point. Otherwise, output "NO".

Sample Input

2 
1 1 1 
3 4 6

Sample Output

YES 0.5000 
YES 2.0000

Hint

Source

“浪潮杯”山东省第六届ACM大学生程序设计竞赛