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Spheres intersection

Time limit = 2 second(s)

You are give set of closed (closed = contain boundary) spheres in 3-dimentional euclidian space. You should check if they have common point.

Input. The fist line contains number of spheres N, 1 < N ≤ 20, and then N lines go, each with four integer numbers Xi Yi Zi and Ri. All numbers less than 10000 in their absolute value.

Output. YES or NO.

Input#1
2
0 0 0 1
0 0 2 1
Output#1
YES
Input#2
2
0 0 0 1
2 2 2 2
Output#2
NO
Input#3
4
0 0 0 3
0 0 4 3
0 5 0 4
0 6 0 5
Output#3
YES
Input#4
4
0 0 0 3
0 0 4 3
0 5 0 4
0 6 0 4
Output#4
NO

Author:
Artem Voroztsov, played at regional student personal contest in Moscow, 29 April 2005.
1 May 2005

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