Codeforces Round #135 (Div. 2) D. Choosing Capital for Treeland dfs

D. Choosing Capital for Treeland

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

The country Treeland consists of n cities, some pairs of them are connected with unidirectional roads. Overall there are n - 1 roads in the country. We know that if we don't take the direction of the roads into consideration, we can get from any city to any other one.

The council of the elders has recently decided to choose the capital of Treeland. Of course it should be a city of this country. The council is supposed to meet in the capital and regularly move from the capital to other cities (at this stage nobody is thinking about getting back to the capital from these cities). For that reason if city a is chosen a capital, then all roads must be oriented so that if we move along them, we can get from city a to any other city. For that some roads may have to be inversed.

Help the elders to choose the capital so that they have to inverse the minimum number of roads in the country.

Input

The first input line contains integer n (2 ≤ n ≤ 2·105) — the number of cities in Treeland. Next n - 1 lines contain the descriptions of the roads, one road per line. A road is described by a pair of integers si, ti (1 ≤ si, ti ≤ n; si ≠ ti) — the numbers of cities, connected by that road. The i-th road is oriented from city si to city ti. You can consider cities in Treeland indexed from 1 to n.

Output

In the first line print the minimum number of roads to be inversed if the capital is chosen optimally. In the second line print all possible ways to choose the capital — a sequence of indexes of cities in the increasing order.

Examples

input

3
2 1
2 3

output

0
2 

input

4
1 4
2 4
3 4

output

2
1 2 3 

题意：给你一棵树，有一个有向边，以一个点为根形成一棵树，求逆转的边数最小的所有根；

思路：以任意节点为根，dfs一遍求答案；正的边权为0，需要逆转的边权为1；

　　   改成另外一个点的答案，即需要修改该点到根的这条链，ans-1的数目+0的数目；

　　　两边dfs；

#pragma comment(linker, "/STACK:1024000000,1024000000")
#include<iostream>
#include<cstdio>
#include<cmath>
#include<string>
#include<queue>
#include<algorithm>
#include<stack>
#include<cstring>
#include<vector>
#include<list>
#include<bitset>
#include<set>
#include<map>
#include<time.h>
using namespace std;
#define LL long long
#define pb push_back
#define mkp make_pair
#define pi (4*atan(1.0))
#define eps 1e-8
#define bug(x)  cout<<"bug"<<x<<endl;
const int N=2e5+10,M=2e6+10,inf=1e9+10;
const LL INF=1e18+10,mod=998244353,MOD=998244353;


int dp[N],ans=inf;
vector<pair<int,int> >edge[N];
void dfs(int u,int fa)
{
    dp[u]=0;
    for(int i=0;i<edge[u].size();i++)
    {
        int v=edge[u][i].first;
        int w=edge[u][i].second;
        if(v==fa)continue;
        dfs(v,u);
        dp[u]+=dp[v]+w;
    }
}
void dfs(int u,int fa,int val)
{
    dp[u]=dp[1]-val;
    ans=min(ans,dp[u]);
    for(int i=0;i<edge[u].size();i++)
    {
        int v=edge[u][i].first;
        int w=(edge[u][i].second%2?1:-1);
        if(v==fa)continue;
        dfs(v,u,val+w);
    }
}
int main()
{
    int n;
    scanf("%d",&n);
    for(int i=1;i<n;i++)
    {
        int u,v;
        scanf("%d%d",&u,&v);
        edge[u].pb(mkp(v,0));
        edge[v].pb(mkp(u,1));
    }
    dfs(1,0);
    dfs(1,0,0);
    printf("%d
",ans);
    for(int i=1;i<=n;i++)
        if(ans==dp[i])printf("%d ",i);

    return 0;
}