Codeforces 731C. Socks 联通块

C. Socks

time limit per test：

2 seconds

memory limit per test：

256 megabytes

input：

standard input

output：

standard output

Arseniy is already grown-up and independent. His mother decided to leave him alone for m days and left on a vacation. She have prepared a lot of food, left some money and washed all Arseniy's clothes.

Ten minutes before her leave she realized that it would be also useful to prepare instruction of which particular clothes to wear on each of the days she will be absent. Arseniy's family is a bit weird so all the clothes is enumerated. For example, each of Arseniy's n socks is assigned a unique integer from 1 to n. Thus, the only thing his mother had to do was to write down two integers li and ri for each of the days — the indices of socks to wear on the day i (obviously, li stands for the left foot and ri for the right). Each sock is painted in one of kcolors.

When mother already left Arseniy noticed that according to instruction he would wear the socks of different colors on some days. Of course, that is a terrible mistake cause by a rush. Arseniy is a smart boy, and, by some magical coincidence, he posses k jars with the paint — one for each of k colors.

Arseniy wants to repaint some of the socks in such a way, that for each of m days he can follow the mother's instructions and wear the socks of the same color. As he is going to be very busy these days he will have no time to change the colors of any socks so he has to finalize the colors now.

The new computer game Bota-3 was just realised and Arseniy can't wait to play it. What is the minimum number of socks that need their color to be changed in order to make it possible to follow mother's instructions and wear the socks of the same color during each of mdays.

Input

The first line of input contains three integers n, m and k (2 ≤ n ≤ 200 000, 0 ≤ m ≤ 200 000, 1 ≤ k ≤ 200 000) — the number of socks, the number of days and the number of available colors respectively.

The second line contain n integers c1, c2, ..., cn (1 ≤ ci ≤ k) — current colors of Arseniy's socks.

Each of the following m lines contains two integers li and ri (1 ≤ li, ri ≤ n, li ≠ ri) — indices of socks which Arseniy should wear during the i-th day.

Output

Print one integer — the minimum number of socks that should have their colors changed in order to be able to obey the instructions and not make people laugh from watching the socks of different colors.

Examples

input

3 2 3
1 2 3
1 2
2 3

output

2

input

3 2 2
1 1 2
1 2
2 1

output

0

Note

In the first sample, Arseniy can repaint the first and the third socks to the second color.

In the second sample, there is no need to change any colors.

题目连接：http://codeforces.com/contest/731/problem/C

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题意：有n只袜子，每只袜子的颜色为c[i]。m天，每天穿第li，ri只袜子。在m天之前改变袜子的颜色，问至少需要改变多少只袜子的颜色，才能是的每天穿一样颜色的袜子。

思路：联通块。求有多少个联通块。可以用搜索，也可以用并查集。每个联通块里面的袜子颜色必须一样。把联通块里面的袜子颜色全部变成出现次数最多的颜色。注意：如果只用cou数组表示联通块里面颜色出现的次数，那么每次搜索之前都必须初始化数组cou，这样的话就会超时。可以加一个set表示当前联通块里面的颜色，如果颜色x没有出现过，则cou[x]=1,否者cou[x]++。然后再把颜色x入set。这样的话就不需要每次都初始化cou数组了，因为可以通过set来初始化单一的cou[x]，那么只需要每次初始化set就可以了。

代码：

#include<bits/stdc++.h>
using namespace std;
const int MAXN=3e5+100;
int c[MAXN];
vector<int>edge[MAXN];
int sign[MAXN];
set<int>s;
int cou[MAXN];
int cnt=0,Max=0;
void dfs(int i)
{
    sign[i]=1;
    if(s.count(c[i])==0) cou[c[i]]=1;
    else cou[c[i]]++;
    s.insert(c[i]);
    cnt++;
    Max=max(Max,cou[c[i]]);
    for(int j=0; j<edge[i].size(); j++)
    {
        if(sign[edge[i][j]]==0)
            dfs(edge[i][j]);
    }
}
int main()
{
    int i,j,n,m,k;
    scanf("%d%d%d",&n,&m,&k);
    for(i=1; i<=n; i++) scanf("%d",&c[i]);
    for(i=1; i<=m; i++)
    {
        int u,v;
        scanf("%d%d",&u,&v);
        edge[u].push_back(v);
        edge[v].push_back(u);
    }
    int ans=0;
    for(i=1;i<=n;i++)
    {
        if(sign[i]!=0) continue;
        cnt=Max=0;
        s.clear();
        dfs(i);
        ans+=cnt-Max;
    }
    cout<<ans<<endl;
    return 0;
}