#include <bits/stdc++.h>
using namespace std;
vector<vector<pair<int, int>>> xy(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_x(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_xr(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_y(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_yr(3, vector<pair<int, int>>());
int n;
int A[6] = {0, 0, 1, 1, 2, 2};
int B[6] = {1, 2, 0, 2, 0, 1};
int C[6] = {2, 1, 2, 0, 1, 0};
const int inf = 1 << 30;
bool yy(pair<int, int> &lhs, pair<int, int> &rhs) {
  return lhs.second < rhs.second;
}
bool yy_r(pair<int, int> &lhs, pair<int, int> &rhs) {
  return lhs.second > rhs.second;
}
bool ok(int z) {
  int a, b, c, x, y, max_x, max_y, flg, cnt;
  for (int i = 0; i < 6; i++) {
    a = A[i];
    b = B[i];
    c = C[i];
    max_x = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_x[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_y[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_x = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_x[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    max_y = -inf;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_x = inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_xr[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x--;
    max_y = -inf;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_y[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    max_x = -inf;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_yr[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y <= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y--;
    max_x = -inf;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y <= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y <= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
  }
  return false;
}
int main(void) {
  cin >> n;
  int x, y, c;
  for (int i = 0; i < n; i++) {
    cin >> x >> y >> c;
    xy[c - 1].push_back({x, y});
  }
  for (int i = 0; i < 3; i++) {
    sort(xy[i].begin(), xy[i].end());
    xy_x[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), greater<pair<int, int>>());
    xy_xr[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), yy);
    xy_y[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), yy_r);
    xy_yr[i] = xy[i];
  }
  int l, r, mid;
  l = 1;
  r = n + 1;
  while (r - l > 1) {
    mid = (l + r) / 2;
    if (ok(mid))
      l = mid;
    else
      r = mid;
  }
  cout << 3 * l << "\n";
}

### Prompt

Please create a solution in CPP to the following problem:

On an endless checkered sheet of paper, n cells are chosen and colored in three colors, where n is divisible by 3. It turns out that there are exactly n/3 marked cells of each of three colors! 

Find the largest such k that it's possible to choose k/3 cells of each color, remove all other marked cells, and then select three rectangles with sides parallel to the grid lines so that the following conditions hold:

  * No two rectangles can intersect (but they can share a part of the boundary). In other words, the area of intersection of any two of these rectangles must be 0.
  * The i-th rectangle contains all the chosen cells of the i-th color and no chosen cells of other colors, for i = 1, 2, 3. 

Input

The first line of the input contains a single integer n — the number of the marked cells (3 ≤ n ≤ 10^5, n is divisible by 3).

The i-th of the following n lines contains three integers x_i, y_i, c_i (|x_i|,|y_i| ≤ 10^9; 1 ≤ c_i ≤ 3), where (x_i, y_i) are the coordinates of the i-th marked cell and c_i is its color.

It's guaranteed that all cells (x_i, y_i) in the input are distinct, and that there are exactly n/3 cells of each color.

Output

Output a single integer k — the largest number of cells you can leave.

Examples

Input


9
2 3 1
4 1 2
2 1 3
3 4 1
5 3 2
4 4 3
2 4 1
5 2 2
3 5 3


Output


6


Input


3
1 1 1
2 2 2
3 3 3


Output


3

Note

In the first sample, it's possible to leave 6 cells with indexes 1, 5, 6, 7, 8, 9.

In the second sample, it's possible to leave 3 cells with indexes 1, 2, 3.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
vector<vector<pair<int, int>>> xy(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_x(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_xr(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_y(3, vector<pair<int, int>>());
vector<vector<pair<int, int>>> xy_yr(3, vector<pair<int, int>>());
int n;
int A[6] = {0, 0, 1, 1, 2, 2};
int B[6] = {1, 2, 0, 2, 0, 1};
int C[6] = {2, 1, 2, 0, 1, 0};
const int inf = 1 << 30;
bool yy(pair<int, int> &lhs, pair<int, int> &rhs) {
  return lhs.second < rhs.second;
}
bool yy_r(pair<int, int> &lhs, pair<int, int> &rhs) {
  return lhs.second > rhs.second;
}
bool ok(int z) {
  int a, b, c, x, y, max_x, max_y, flg, cnt;
  for (int i = 0; i < 6; i++) {
    a = A[i];
    b = B[i];
    c = C[i];
    max_x = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_x[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_y[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_x = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_x[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    max_y = -inf;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_x = inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_xr[a]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x--;
    max_y = -inf;
    for (auto tmp : xy_y[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    for (auto tmp : xy_y[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x <= max_x && y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = -inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_y[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y >= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y++;
    max_x = -inf;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y >= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
    max_y = inf;
    flg = 0;
    cnt = 0;
    for (auto tmp : xy_yr[a]) {
      x = tmp.first;
      y = tmp.second;
      if (y <= max_y) {
        max_y = y;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_y--;
    max_x = -inf;
    for (auto tmp : xy_x[b]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y <= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    cnt = 0;
    max_x++;
    for (auto tmp : xy_x[c]) {
      x = tmp.first;
      y = tmp.second;
      if (x >= max_x && y <= max_y) {
        max_x = x;
        cnt++;
        if (cnt == z) {
          flg++;
          break;
        }
      }
    }
    if (flg == 3) return true;
  }
  return false;
}
int main(void) {
  cin >> n;
  int x, y, c;
  for (int i = 0; i < n; i++) {
    cin >> x >> y >> c;
    xy[c - 1].push_back({x, y});
  }
  for (int i = 0; i < 3; i++) {
    sort(xy[i].begin(), xy[i].end());
    xy_x[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), greater<pair<int, int>>());
    xy_xr[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), yy);
    xy_y[i] = xy[i];
    sort(xy[i].begin(), xy[i].end(), yy_r);
    xy_yr[i] = xy[i];
  }
  int l, r, mid;
  l = 1;
  r = n + 1;
  while (r - l > 1) {
    mid = (l + r) / 2;
    if (ok(mid))
      l = mid;
    else
      r = mid;
  }
  cout << 3 * l << "\n";
}

```