#include <bits/stdc++.h>
using namespace std;
/*{{{*/  //template
#define rep(i,n) for(int i=0;i<(int)(n);i++)
constexpr int INF = numeric_limits<int>::max()/2;
constexpr long long LINF = numeric_limits<long long>::max()/3;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr<<#x<<":"<<x<<endl
#define debug2(x,y) cerr<<#x<<","<<#y":"<<x<<","<<y<<endl
//struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double{ double d; explicit Double(double x) : d(x){} };
ostream& operator<<(ostream& os,const Double x){ os << fixed << setprecision(20) << x.d; return os; }
template<typename T> ostream& operator<<(ostream& os,const vector<T>& vec){ os << "["; for(const auto& v : vec){ os << v << ","; } os << "]"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os,const pair<T,U>& p){ os << "(" << p.first << ","<< p.second <<")"; return os; }
template<typename T> ostream& operator<<(ostream& os,const set<T>& st){ os<<"{"; for(T v:st) os<<v<<","; os <<"}"; return os; }
template<typename T,typename U> inline void chmax(T &x,U y){ if(y>x) x = y; }
template<typename T,typename U> inline void chmin(T &x,U y){ if(y<x) x = y; }
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
ll gcd(ll a,ll b){ if(b==0) return a; else return gcd(b,a%b); }
//constexpr double eps = 1e-14; 
constexpr double eps = 1e-10; 
constexpr ll mod = 1e9+7;
const int dx[]={1,0,-1,0} ,dy[] = {0,1,0,-1};
/*}}}*/

int main(){
    int N;
    cin >> N;
    vector<ll> a(N);
    rep(i,N) cin >> a[i];

    vector<ll> b(N);
    map<ll,ll> z;
    for(int i=0;i<N;i++){
        if(z.count(a[i])) continue;
        z[a[i]] = i;
    }

    for(int i=0;i<N;i++) b[i] = z[a[i]];

    set<int> tmp;

    vector<int> ans;

    //debug(b);

    vector<ll> cnt(N+1,0);
    for(int i=0;i<N;i++){
        cnt[b[i]]++;
        cnt[b[N-1-i]]--;
        if(cnt[b[i]] != 0) tmp.insert(b[i]);
        else tmp.erase(b[i]);

        if(cnt[b[N-1-i]] != 0) tmp.insert(b[N-i-1]);
        else tmp.erase(b[N-i-1]);

        if(tmp.size() == 0){
            ans.push_back(i+1);
        }
    }

    for(int i=0;i<ans.size();i++){
        cout << ans[i];
        if(i==ans.size()-1) cout << endl;
        else cout <<  " ";
    }
}


### Prompt

Create a solution in Cpp for the following problem:

problem

Given a sequence $ a_i $ of length $ N $. Output all integers $ K (1 \ le K \ le N) $ that satisfy the following conditions.

Condition: Well sorted $ a_1, \ cdots, a_K $ matches $ a_ {N-K + 1}, \ cdots, a_N $.





Example

Input

8
5 2 4 9 4 9 2 5


Output

1 2 4 6 7 8

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
/*{{{*/  //template
#define rep(i,n) for(int i=0;i<(int)(n);i++)
constexpr int INF = numeric_limits<int>::max()/2;
constexpr long long LINF = numeric_limits<long long>::max()/3;
#define mp make_pair
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
#define sz(x) (int)(x).size()
#define debug(x) cerr<<#x<<":"<<x<<endl
#define debug2(x,y) cerr<<#x<<","<<#y":"<<x<<","<<y<<endl
//struct fin{ fin(){ cin.tie(0); ios::sync_with_stdio(false); } } fin_;
struct Double{ double d; explicit Double(double x) : d(x){} };
ostream& operator<<(ostream& os,const Double x){ os << fixed << setprecision(20) << x.d; return os; }
template<typename T> ostream& operator<<(ostream& os,const vector<T>& vec){ os << "["; for(const auto& v : vec){ os << v << ","; } os << "]"; return os; }
template<typename T,typename U> ostream& operator<<(ostream& os,const pair<T,U>& p){ os << "(" << p.first << ","<< p.second <<")"; return os; }
template<typename T> ostream& operator<<(ostream& os,const set<T>& st){ os<<"{"; for(T v:st) os<<v<<","; os <<"}"; return os; }
template<typename T,typename U> inline void chmax(T &x,U y){ if(y>x) x = y; }
template<typename T,typename U> inline void chmin(T &x,U y){ if(y<x) x = y; }
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<vi> vvi;
ll gcd(ll a,ll b){ if(b==0) return a; else return gcd(b,a%b); }
//constexpr double eps = 1e-14; 
constexpr double eps = 1e-10; 
constexpr ll mod = 1e9+7;
const int dx[]={1,0,-1,0} ,dy[] = {0,1,0,-1};
/*}}}*/

int main(){
    int N;
    cin >> N;
    vector<ll> a(N);
    rep(i,N) cin >> a[i];

    vector<ll> b(N);
    map<ll,ll> z;
    for(int i=0;i<N;i++){
        if(z.count(a[i])) continue;
        z[a[i]] = i;
    }

    for(int i=0;i<N;i++) b[i] = z[a[i]];

    set<int> tmp;

    vector<int> ans;

    //debug(b);

    vector<ll> cnt(N+1,0);
    for(int i=0;i<N;i++){
        cnt[b[i]]++;
        cnt[b[N-1-i]]--;
        if(cnt[b[i]] != 0) tmp.insert(b[i]);
        else tmp.erase(b[i]);

        if(cnt[b[N-1-i]] != 0) tmp.insert(b[N-i-1]);
        else tmp.erase(b[N-i-1]);

        if(tmp.size() == 0){
            ans.push_back(i+1);
        }
    }

    for(int i=0;i<ans.size();i++){
        cout << ans[i];
        if(i==ans.size()-1) cout << endl;
        else cout <<  " ";
    }
}


```