A toll-road network connects n towns, numbered 0 to n - 1, with m two-way roads. Road i connects towns u and v and charges a toll of w to use. A driver cares about the single WORST (highest) toll paid on their route, since that is the most they will ever be charged at one booth.

Given a starting town s and a destination town t (with s != t), print the smallest possible value of the worst toll along any route from s to t (i.e., choose the route that minimizes its own maximum toll). If t is unreachable from s, print -1 instead.

Input format

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

Output format

A single integer: the minimum possible value of the worst toll along a route 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 3
2 3 4
0 3

4

3 1
0 1 6
0 2

-1