Codeforces Beta Round #29 (Div. 2, Codeforces format) C. Mail Stamps 拓扑排序

C. Mail Stamps

 

 

One day Bob got a letter in an envelope. Bob knows that when Berland's post officers send a letter directly from city «A» to city «B», they stamp it with «A B», or «B A». Unfortunately, often it is impossible to send a letter directly from the city of the sender to the city of the receiver, that's why the letter is sent via some intermediate cities. Post officers never send a letter in such a way that the route of this letter contains some city more than once. Bob is sure that the post officers stamp the letters accurately.

There are n stamps on the envelope of Bob's letter. He understands that the possible routes of this letter are only two. But the stamps are numerous, and Bob can't determine himself none of these routes. That's why he asks you to help him. Find one of the possible routes of the letter.

Input

The first line contains integer n (1 ≤ n ≤ 105) — amount of mail stamps on the envelope. Then there follow n lines with two integers each — description of the stamps. Each stamp is described with indexes of the cities between which a letter is sent. The indexes of cities are integers from 1 to 109. Indexes of all the cities are different. Every time the letter is sent from one city to another, exactly one stamp is put on the envelope. It is guaranteed that the given stamps correspond to some valid route from some city to some other city.

Output

Output n + 1 numbers — indexes of cities in one of the two possible routes of the letter.

Examples

input

2
1 100
100 2

output

2 100 1 

input

3
3 1
100 2
3 2

output

100 2 3 1 

题意：

　　给你n张邮票

　　每张邮票上面写有两个城市a,b

　　有可能是a到b

　　也有可能是b到a

     现在问你 一条可行的路线

题解：

　　很明显的拓扑

　　每次选择度小于等于1 的点加入答案就好了

　　注意数据范围

#include <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include<vector>
#include<map>
#include<queue>
using namespace std;
const int N = 1e5+10, M = 30005, mod = 1000000007, inf = 0x3f3f3f3f;
typedef long long ll;

int n,a[N],b[N],vis[N],cnt = 1;
vector<int > G[N];
map<int,int > mp,hash,fhash;
int main() {
    scanf("%d",&n);
    for(int i=1;i<=n;i++) {
        scanf("%d%d",&a[i],&b[i]);
        if(!hash.count(a[i])) hash[a[i]] = cnt ,fhash[cnt++] = a[i];
         if(!hash.count(b[i])) hash[b[i]] = cnt, fhash[cnt++] = b[i];
         a[i] = hash[a[i]];
         b[i] = hash[b[i]];
    }
    for(int i=1;i<=n;i++) {
        int aa = a[i], bb = b[i];
        G[aa].push_back(bb);
        G[bb].push_back(aa);
        mp.count(aa)?mp[aa]++:mp[aa]=1;
        mp.count(bb)?mp[bb]++:mp[bb]=1;
    }
    int u = 0;
    for(map<int,int >::iterator it=mp.begin();it!=mp.end();it++) {
        int now = it->first;
        if(mp[now]==1) u = now;
    }
    queue<int> q;
    vector<int >ans;
    q.push(u);
   // cout<<fhash[u]<<endl;
    memset(vis,0,sizeof(vis));
    while(!q.empty()) {
        int k = q.front();
        q.pop();
        vis[k] = 1;
        ans.push_back(k);
        for(int i=0;i<G[k].size();i++) {
            //if(vis[G[k][i]]) continue;
            mp[G[k][i]] --;
            if(mp[G[k][i]]<=1&&!vis[G[k][i]]) q.push(G[k][i]);
        }
    }
    for(int i=0;i<ans.size();i++) {
            //cout<<ans[i]<<endl;
        printf("%d ",fhash[ans[i]]) ;
    }
    return 0;
}