#include <bits/stdc++.h>
using namespace std;
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

//#define int long long
// typedef __int128_t Int;
#define DBG 1
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define loop(n) rep(loop, (0), (n))
#define all(c) begin(c), end(c)
const int INF =
    sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
const double PI = acos(-1);
const double EPS = 1e-9;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  int N;
  cin >> N;
  vector<int> v(N);
  rep(i, 0, N) { cin >> v[i]; }
  map<int, int> p, q;
  vector<int> ans;
  rep(i, 0, N) {
    p[v[i]]++, q[v[N - 1 - i]]++;
    if (p == q)
      ans.push_back(i + 1);
  }
  rep(i, 0, ans.size()) cout << ans[i] << (i == ans.size() - 1 ? '\n' : ' ');

  return 0;
}


### Prompt

Please provide a CPP coded solution to the problem described below:

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;
#ifdef _DEBUG
#define _GLIBCXX_DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

//#define int long long
// typedef __int128_t Int;
#define DBG 1
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = (b)-1; i >= (a); i--)
#define loop(n) rep(loop, (0), (n))
#define all(c) begin(c), end(c)
const int INF =
    sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9) + 7;
const double PI = acos(-1);
const double EPS = 1e-9;
template <class T> bool chmax(T &a, const T &b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> bool chmin(T &a, const T &b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}

signed main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(12);

  int N;
  cin >> N;
  vector<int> v(N);
  rep(i, 0, N) { cin >> v[i]; }
  map<int, int> p, q;
  vector<int> ans;
  rep(i, 0, N) {
    p[v[i]]++, q[v[N - 1 - i]]++;
    if (p == q)
      ans.push_back(i + 1);
  }
  rep(i, 0, ans.size()) cout << ans[i] << (i == ans.size() - 1 ? '\n' : ' ');

  return 0;
}


```