Wells

Hyunsung wants to install wells in villages for African children who cannot drink as much water as they need.

Each village needs a different number of wells. Installing one well in village A counts as one well for village A and for every village connected to A directly by a road. You may install several wells in the same village.

For example, suppose village A is connected to B and to C, and villages A, B, and C need 5, 10, and 7 wells respectively. If you install 5 wells in village A, villages B and C also have 5 wells each counted toward their needs.

Hyunsung donates a lot, so he does not have much money. There are $n$ villages, village $i$ needs at least $W_i$ wells ($W_1, W_2, \ldots, W_n$), and there are $m$ roads between villages. Find the minimum total number of wells to install so that every village's requirement is met.

The first line contains the number of villages $n$ ($1 \le n \le 100{,}000$) and the number of roads $m$ ($1 \le m < 100{,}000$).

The second line contains the minimum number of wells each village needs, $W_1, W_2, \ldots, W_n$ ($0 \le W_i \le 10{,}000{,}000$).

Each of the next $m$ lines describes a road with two village numbers $a$ and $b$ that the road connects. Villages are numbered from $1$ to $n$, and there is exactly one path between any two villages.

Print the minimum number of wells to install on the first line.