A976.Wormhole Sort--Silver

Farmer John's cows have grown tired of his daily request that they sort
themselves before leaving the barn each morning. They have just completed
their PhDs in quantum physics, and are ready to speed things up a bit.
This morning, as usual, Farmer John's $N$ cows ($1 \leq N \leq 10^5$),
conveniently numbered $1 \dots N$, are scattered throughout the barn at $N$
distinct locations, also numbered $1 \dots N$, such that cow $i$ is at
location $p_i$. But this morning there are also $M$ wormholes ($1 \leq M \leq 10^5$), numbered $1 \dots M$, where wormhole $i$ bidirectionally connects
location $a_i$ with location $b_i$, and has a width $w_i$ ($1\le a_i,b_i\le N, a_i\neq b_i, 1\le w_i\le 10^9$).
At any point in time, two cows located at opposite ends of a wormhole may
choose to simultaneously swap places through the wormhole. The cows must
perform such swaps until cow $i$ is at location $i$ for $1 \leq i \leq N$.
The cows are not eager to get squished by the wormholes. Help them maximize
the width of the least wide wormhole which they must use to sort themselves.
It is guaranteed that it is possible for the cows to sort themselves.

• Test cases 3-5 satisfy $N,M\le 1000.$
• Test cases 6-10 satisfy no additional constraints.

The first line contains two integers, $N$ and $M$.
The second line contains the $N$ integers $p_1, p_2, \dots, p_N$. It is
guaranteed that $p$ is a permutation of $1\ldots N.$
For each $i$ between $1$ and $M$, line $i+2$ contains the integers $a_i$,
$b_i$, and $w_i$.

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