【Educational Codeforces Round 33】 C. Rumor (并查集)

C. Rumor

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

Vova promised himself that he would never play computer games... But recently Firestorm — a well-known game developing company — published their newest game, World of Farcraft, and it became really popular. Of course, Vova started playing it.

Now he tries to solve a quest. The task is to come to a settlement named Overcity and spread a rumor in it.

Vova knows that there are n characters in Overcity. Some characters are friends to each other, and they share information they got.
Also Vova knows that he can bribe each character so he or she starts spreading the rumor; i-th character wants ci gold
in exchange for spreading the rumor. When a character hears the rumor, he tells it to all his friends, and they start spreading the rumor to their friends (for free), and so on.

The quest is finished when all n characters know the rumor. What is the minimum amount of gold Vova needs to spend in order to finish
the quest?

Take a look at the notes if you think you haven't understood the problem completely.

Input

The first line contains two integer numbers n and m (1 ≤ n ≤ 105, 0 ≤ m ≤ 105)
— the number of characters in Overcity and the number of pairs of friends.

The second line contains n integer numbers ci (0 ≤ ci ≤ 109)
— the amount of gold i-th character asks to start spreading the rumor.

Then m lines follow, each containing a pair of numbers (xi, yi)
which represent that characters xi and yi are
friends (1 ≤ xi, yi ≤ n, xi ≠ yi).
It is guaranteed that each pair is listed at most once.

Output

Print one number — the minimum amount of gold Vova has to spend in order to finish the quest.

Examples

input

5 2
2 5 3 4 8
1 4
4 5

output

10

input

10 0
1 2 3 4 5 6 7 8 9 10

output

55

input

10 5
1 6 2 7 3 8 4 9 5 101 2
3 4
5 6
7 8
9 10

output

15

Note

In the first example the best decision is to bribe the first character (he will spread the rumor to fourth character, and the fourth one will spread it to fifth). Also Vova has to bribe the second and the third characters, so they know the rumor.

In the second example Vova has to bribe everyone.

In the third example the optimal decision is to bribe the first, the third, the fifth, the seventh and the ninth characters.

#include <bits/stdc++.h>
using namespace std;
int p[100005], a[100005], cnt[100005];
int findset(int x){
return p[x] == x ? x : p[x] = findset(p[x]);
}
int main(){
int n, m;
cin >> n >> m;
for(int i = 1; i <= n; ++i){
p[i] = i;
}
for(int i = 1; i <= n; ++i){
scanf("%d", &a[i]);
}
int x, y;
for(int i = 1; i <= m; ++i){
scanf("%d %d", &x, &y);
p[findset(x)] = findset(y);
}
long long ans = 0;
memset(cnt, 0, sizeof(cnt));
for(int i = 1; i <= n; ++i){
if(findset(i) == i){
cnt[i] = 1e9;
}
}
for(int i = 1; i <= n; ++i){
cnt[findset(i)] = min(cnt[findset(i)], a[i]);
}
for(int i = 1; i <= n; ++i){
if(findset(i) == i){
ans += cnt[i];
}
}
cout<<ans<<endl;
}

/*
题意：
每个字母传递一个人有一个代价，朋友之间传递不需要代价，问所有人都被传到需要多少代价。

思路：
并查集处理朋友关系，对于一个集合只需要传递给大家最小的那个人，然后让他传递给他的所有朋友，
把所有集合的最小值加起来即可。
*/