A monitoring signal spreads through a network of n hubs, numbered 0 to n - 1, along m one-way links. Link i goes from hub u to hub v and takes w time units to propagate the signal from u to v. The signal originates at a given source hub at time 0. A hub other than the source has "received" the signal once the fastest possible propagation delay from the source to that hub has elapsed.

Given a deadline D, print the number of hubs (not counting the source itself) that have received the signal at or before time D.

Input format

Line 1: two integers n m. Next m lines: three integers u v w -- a directed link from hub u to hub v with propagation delay w (hubs are 0-indexed). Last line: two integers s D -- the source hub and the deadline.

Output format

A single integer: the number of hubs other than s whose fastest propagation delay from s is at most D.

Constraints

• 1 <= n <= 1000
• 0 <= m <= 4000
• 0 <= u, v < n, u != v
• 1 <= w <= 1000
• 0 <= s < n
• 0 <= D <= 1000000

4 4
0 1 3
0 2 10
1 2 2
2 3 4
0 5

2

3 1
0 1 5
0 2

0