A highlevel international rally championship is about to be held. The rules of the race state that the race is held on ordinary roads and the route has a fixed length. You are given a map of the cities and twoway roads connecting it. To make the race safer it is held on oneway roads. The race may start and finish anyplace on the road. Determine if it is possible to make a route having a given length S.
Input
The first line of the input contains integers M, N and S that are the number of cities, the number of roads the length of the route (1 ≤ M ≤ 100; 1 ≤ N ≤ 10 000; 1 ≤ S ≤ 2 · 10^{6}).
The following N lines describe the roads as triples of integers: P, Q, R. Here P and Q are cities connected with a road, and R is the length of this road. All numbers satisfy the following restrictions: 1 ≤ P, Q ≤ M; 1 ≤ R ≤ 32000.
Output
Write YES to the output if it is possible to make a required route and NO otherwise. Note that answer must be written in capital Latin letters.
Samples
input  output 

3 2 20
1 2 10
2 3 5
 NO

3 3 1000
1 2 1
2 3 1
1 3 1
 YES

Problem Source: 20022003 ACM Central Region of Russia Quarterfinal Programming Contest, Rybinsk, October 2002