A wireless mesh network has n nodes, numbered 0 to n - 1, and m two-way links. Link i connects nodes u and v and can carry w units of bandwidth. Data sent along a multi-hop route can only flow as fast as the slowest (minimum-bandwidth) link on that route.

Given a source node s and a destination node t (with s != t), print the highest achievable end-to-end bandwidth over any route from s to t, where a route's bandwidth is the minimum link weight along it. If t cannot be reached from s, print -1 instead.

Input format

Line 1: two integers n m. Next m lines: three integers u v w -- an undirected link between nodes u and v with bandwidth w (nodes are 0-indexed). Last line: two integers s t.

Output format

A single integer: the maximum possible end-to-end bandwidth from s to t, or -1 if unreachable.

Constraints

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

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

4

3 1
0 1 7
0 2

-1