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The marathon takes place in the beautiful city of Pordenone, which is formed by $N$ intersections and $M$ bidirectional roads. Each road is exactly $w_i$ meters long.
The marathon starts at intersection $0$ and ends at intersection $N-1$. Marathoners must go through $K$ checkpoints S[0], S[1] ... S[K-1], however, they can run through any route between two consecutive checkpoints.
The marathon starts at intersection $0$ and ends at intersection $N-1$. Marathoners must go through $K$ checkpoints $S[0], S[1] ... S[K-1]$, however, they can run through any route between two consecutive checkpoints.
William's plan is the following:
* $1 ≤ N ≤ 500$
* $1 ≤ M ≤ N * (N-1) / 2$
* $0 ≤ K ≤ N-2$, $K$ even.
* $0 ≤ u, v ≤ N-1$
* $0 &le u, v ≤ N-1$
* $0 ≤ w ≤ 10^9$
* For tests worth $25$ points, $K$ = $0$.
* For tests worth $35$ more points, $0 ≤ K ≤ 18$
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