CodeForces

题目：

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 31 2 31 22 3

output

2

input

3 2 21 1 21 22 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.

思路：

题目给了一个n,m,k分别代表有n只袜子，要穿m天，一共有k种颜色的染料，接下来一行是袜子的颜色，然后接下来有m行，代表了他第几天左脚右脚穿的袜子的颜色，现在要在同一天穿同一种颜色的袜子，那么他就需要对袜子进行染色，每一次可以对一只袜子进行染色，问的是最少染色次。

解法是把在同一天穿的袜子利用并查集放在一起，然后找到颜色相同最多的数量，然后把剩下的染色就可以了.

代码：

#include <cstdio>#include <cstring>#include <cctype>#include <string>#include <set>#include <iostream>#include <map>#include <stack>#include <cmath>#include <queue>#include <vector>#include <algorithm>#define mem(a,b) memset(a,b,sizeof(a))#define inf 0x3f3f3f3f3f3f3f3f#define mod 1000007#define N 200000+20#define M 100000+50#define ll long longusing namespace std;int n,m,k;int a[N],pre[N];vector<int>v[N];void init(){for(int i=1; i<=n; i++)pre[i]=i;}int find(int x){if(x==pre[x])return x;else{pre[x]=find(pre[x]);return pre[x];}}void mix(int x,int y){int fx=find(x);int fy=find(y);if(fx!=fy)pre[fy]=fx;}int main(){int x,y;scanf("%d%d%d",&n,&m,&k);init();for(int i=1; i<=n; i++)scanf("%d",&a[i]);//目前的颜色for(int i=1; i<=m; i++){scanf("%d%d",&x,&y);//读入每天穿的颜色，并且加入并查集mix(x,y);}for(int i=1; i<=n; i++)v[find(i)].push_back(a[i]);//把对应袜子加入集合int ans=0;for(int i=1; i<=n; i++){if(v[i].size()<=1)continue;map<int,int>mp;int maxx=0;for(int j=0; j<v[i].size(); j++){mp[v[i][j]]++;maxx=max(maxx,mp[v[i][j]]);}ans+=v[i].size()-maxx;}printf("%d\n",ans);return 0;}