Given two circles with centers at (x1, y1) and (x2, y2) and having radius r1 and r2 respectively, find if they intersect or not. Two circles are considered to be intersecting if they have a common area. Even if two circles touch at a point then they are considered to be intersecting.

Input

First line contains an integer T. Then follow T lines each line containing integers x1, y1, x2, y2, r1, r2 in that order.

Output

Print "YES" (without quotes) if they intersect and "NO" if they don't intersect.

Constraints

T <= 10,000

All other integers will have an absolute value <= 1000,000,000

Example

Input:
3
0 0 2 2 1 1
0 0 2 2 3 3
0 0 1000000000 0 600000000 400000000

Output:
NO
YES
YES