For their physical fitness program, $N$ $(2 \le N \le 1,000,000)$ cows have decided to run a relay race using the $T$ $(2 \le T \le 100)$ cow trails throughout the pasture.

Each trail connects two different intersections $(1 \le I1_i \le 1,000; 1 \le I2_i \le 1,000)$, each of which is the termination for at least two trails. The cows know the $length_i$ of each trail $(1 \le length_{i} \le 1,000)$, the two intersections the trail connects, and they know that no two intersections are directly connected by two different trails. The trails form a structure known mathematically as a graph.

To run the relay, the $N$ cows position themselves at various intersections (some intersections might have more than one cow). They must position themselves properly so that they can hand off the baton cow-by-cow and end up at the proper finishing place.

Write a program to help position the cows. Find the shortest path that connects the starting intersection ($S$) and the ending intersection ($E$) and traverses exactly $N$ cow trails.

Input

• Line 1: Four space-separated integers: $N$, $T$, $S$, and $E$
• Lines $2..T+1$: Line $i+1$ describes trail $i$ with three space-separated integers: $length_i$, $I1_i$, and $I2_i$

Output

• Line 1: A single integer that is the shortest distance from intersection $S$ to intersection $E$ that traverses exactly $N$ cow trails.

Examples

Input 1

2 6 6 4
11 4 6
4 4 8
8 4 9
6 6 8
2 6 9
3 8 9

Output 1

10

Problem credits: Erik Bernhardsson, 2003