Problem: For a given set of two-dimensional points S, let's denote its extension E(S) as the result of the following algorithm:

Create another set of two-dimensional points R, which is initially equal to S. Then, while there exist four numbers x_1, y_1, x_2 and y_2 such that (x_1, y_1) ∈ R, (x_1, y_2) ∈ R, (x_2, y_1) ∈ R and (x_2, y_2) ∉ R, add (x_2, y_2) to R. When it is impossible to find such four integers, let R be the result of the algorithm.

Now for the problem itself. You are given a set of two-dimensional points S, which is initially empty. You have to process two types of queries: add some point to S, or remove some point from it. After each query you have to compute the size of E(S).

Input

The first line contains one integer q (1 ≤ q ≤ 3 ⋅ 10^5) — the number of queries.

Then q lines follow, each containing two integers x_i, y_i (1 ≤ x_i, y_i ≤ 3 ⋅ 10^5), denoting i-th query as follows: if (x_i, y_i) ∈ S, erase it from S, otherwise insert (x_i, y_i) into S.

Output

Print q integers. i-th integer should be equal to the size of E(S) after processing first i queries.

Example

Input


7
1 1
1 2
2 1
2 2
1 2
1 3
2 1


Output


1 2 4 4 4 6 3 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
int constexpr NXVAL = 300000, NYVAL = 300000;
int main() {
  std::ios::sync_with_stdio(0);
  std::cin.tie(0);
  int nquery;
  std::cin >> nquery;
  struct edge {
    int x, y;
    bool operator==(edge e) const { return x == e.x && y == e.y; }
  };
  struct edge_hash {
    std::size_t operator()(edge e) const {
      return e.x * (std::size_t)1000000007 + e.y;
    }
  };
  struct DSU {
    struct item {
      int d;
      bool isroot() const { return d < 0; }
      int parent() const {
        assert(!isroot());
        return d;
      }
      int rank() const {
        assert(isroot());
        return -d;
      }
      int ls, rs;
      int64_t val() const {
        assert(isroot());
        return (int64_t)ls * rs;
      }
    };
    std::vector<item> d;
    int64_t val;

   private:
    struct backupitem {
      int index;
      item x;
    };
    std::vector<backupitem> backup;
    void setitem(int i, item x) {
      backup.push_back({i, d[i]});
      d[i] = x;
    }

   public:
    struct state {
      unsigned backup_size;
      int64_t val;
    };
    state getstate() const { return {(unsigned)backup.size(), val}; }
    void reset() {
      d.assign(NXVAL, {-1, 1, 0});
      d.resize(NXVAL + NYVAL, {-1, 0, 1});
      val = 0;
    }
    void restore(state s) {
      while (backup.size() > s.backup_size) {
        auto z = backup.back();
        backup.pop_back();
        d[z.index] = z.x;
      }
      assert(backup.size() == s.backup_size);
      val = s.val;
    }
    int root(int u) { return d[u].isroot() ? u : root(d[u].parent()); }
    void join(int u, int v) {
      u = root(u);
      v = root(v);
      if (u == v) return;
      if (d[u].rank() < d[v].rank()) std::swap(u, v);
      item new_du{d[u].d, d[u].ls + d[v].ls, d[u].rs + d[v].rs};
      if (d[u].rank() == d[v].rank()) --new_du.d;
      val += new_du.val() - d[u].val() - d[v].val();
      setitem(u, new_du);
      setitem(v, {u, 0, 0});
    }
  };
  struct ST {
    std::vector<std::vector<edge>> t;
    ST(int n) : t(2 * n) {}
    void add(int l, int r, edge e) {
      l += int(t.size() / 2);
      r += int(t.size() / 2);
      while (l != r) {
        if (l & 1) t[l++].push_back(e);
        if (r & 1) t[--r].push_back(e);
        l >>= 1;
        r >>= 1;
      }
    }
    std::vector<int64_t> ans;
    DSU d;
    void solve(int i) {
      DSU::state oldstate = d.getstate();
      for (edge e : t[i]) d.join(e.x, e.y);
      if ((unsigned)i >= t.size() / 2) {
        ans[i - t.size() / 2] = d.val;
      } else {
        solve(i << 1);
        solve(i << 1 | 1);
      }
      d.restore(oldstate);
    }
    void solveall() {
      d.reset();
      ans.resize(t.size() / 2);
      solve(1);
    }
  };
  ST tree(nquery);
  {
    std::unordered_map<edge, int, edge_hash> es;
    for (int i = 0; i < nquery; ++i) {
      edge e;
      std::cin >> e.x >> e.y;
      --e.x;
      --e.y;
      e.y += NXVAL;
      auto iter = es.find(e);
      if (iter != es.end()) {
        tree.add(iter->second, i, e);
        es.erase(iter);
      } else {
        es.insert({e, i});
      }
    }
    for (auto edge_starti : es)
      tree.add(edge_starti.second, nquery, edge_starti.first);
  }
  tree.solveall();
  for (auto x : tree.ans) std::cout << x << ' ';
  std::cout << '\n';
}