## CCO '12 P2 - The Hungary Games

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Points: 15
Time limit: 1.0s
Memory limit: 1G

Problem type
##### Canadian Computing Competition: 2012 Stage 2, Day 1, Problem 2

Welcome to the Hungary Games! The streets of Budapest form a twisted network of one-way streets. You have been forced to join a race as part of a "Reality TV" show where you race through these streets, starting at the Szechenyi thermal bath ( for short) and ending at the Tomb of Gul Baba ( for short).

Naturally, you want to complete the race as quickly as possible, because you will get more promotional contracts the better you perform. However, there is a catch: any person who is smart enough to take a shortest - route will be thrown into the Palvolgyi cave system and kept as a national treasure. You would like to avoid this fate, but still be as fast as possible. Write a program that computes a strictly-second-shortest - route.

Sometimes the strictly second-shortest route visits some nodes more than once; see Sample Input 2 for an example.

#### Input Specification

The first line will have the format , where is the number of nodes in Budapest and is the number of edges. The nodes are ; node represents ; node represents . Then there are lines of the form , indicating a one-way street from to of length . You can assume that on these lines, and that the ordered pairs are distinct.

#### Output Specification

Output the length of a strictly-second-shortest route from to . If there are less than two possible lengths for routes from to , output .

#### Limits

Every length will be a positive integer between and . For 50% of the test cases, we will have and . All test cases will have and .

#### Sample Input 1

4 6
1 2 5
1 3 5
2 3 1
2 4 5
3 4 5
1 4 13

#### Output for Sample Input 1

11

#### Explanation for Sample Output 1

There are two shortest routes of length 10 (, ) and the strictly-second-shortest route is with length 11.

#### Sample Input 2

2 2
1 2 1
2 1 1

#### Output for Sample Input 2

3

#### Explanation for Sample Output 2

The shortest route is of length 1, and the strictly-second route is of length 3.