#include <bits/stdc++.h>
using namespace std;
bool home = true;
struct Cell {
  int x;
  int y;
  int type;
};
bool cmp1(Cell a, Cell b) { return a.x < b.x; }
bool cmp2(Cell a, Cell b) { return a.y < b.y; }
const int N = (int)1e5 + 7;
int n;
bool okLR(vector<Cell> &cells, int need, vector<int> ord) {
  int first = ord[0], second = ord[1], third = ord[2];
  int cntFirst = 0;
  for (int i = 0; i < n; i++) {
    if (cells[i].type == first) {
      cntFirst++;
      if (cntFirst == need) {
        int cntSecond = 0;
        for (int j = i + 1; j < n; j++) {
          if (cells[j].x > cells[i].x && cells[j].type == second) {
            cntSecond++;
            if (cntSecond == need) {
              int cntThird = 0;
              for (int k = j + 1; k < n; k++) {
                if (cells[k].x > cells[j].x && cells[k].type == third) {
                  cntThird++;
                  if (cntThird == need) {
                    return true;
                  }
                }
              }
              return false;
            }
          }
        }
        return false;
      }
    }
  }
  assert(false);
}
struct Bbox {
  int xmin = (int)1e9, ymin = (int)1e9;
  int xmax = -(int)1e9, ymax = -(int)1e9;
  int ind;
  void add(int x, int y) {
    xmin = min(xmin, x);
    xmax = max(xmax, x);
    ymin = min(ymin, y);
    ymax = max(ymax, y);
  }
};
bool okUD(vector<Cell> &cells, vector<Cell> &cells2, int need,
          vector<int> ord) {
  int first = ord[0], second = ord[1], third = ord[2];
  int cntFirst = 0;
  for (int i = 0; i < n; i++) {
    if (cells[i].type == first) {
      cntFirst++;
      if (cntFirst == need) {
        int cntSecond = 0;
        for (int j = 0; j < n; j++) {
          if (cells2[j].x > cells[i].x && cells2[j].type == second) {
            cntSecond++;
            if (cntSecond == need) {
              int cntThird = 0;
              for (int k = j + 1; k < n; k++) {
                if (cells2[k].y > cells2[j].y && cells2[k].x > cells[i].x &&
                    cells2[k].type == third) {
                  cntThird++;
                  if (cntThird == need) {
                    return true;
                  }
                }
              }
              return false;
            }
          }
        }
        return false;
      }
    }
  }
  assert(false);
}
void upd(int invx, int invy, vector<int> ord, int &bestK, vector<Cell> cells,
         vector<Cell> cells2) {
  int low = bestK + 1, high = n / 3;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (okLR(cells, mid, ord)) {
      bestK = mid;
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
  low = bestK + 1;
  high = n / 3;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (okUD(cells, cells2, mid, ord)) {
      bestK = mid;
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
}
signed main() {
  if (!home) {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  cin >> n;
  vector<Cell> cells(n);
  for (auto &cell : cells) {
    cin >> cell.x >> cell.y >> cell.type;
  }
  int bestK = 0;
  for (int swp = 0; swp < 2; swp++) {
    for (int invx = 0; invx < 2; invx++) {
      for (int invy = 0; invy < 2; invy++) {
        vector<Cell> cells2;
        if (invx) {
          for (auto &cell : cells) {
            cell.x *= -1;
          }
        }
        if (invy) {
          for (auto &cell : cells) {
            cell.y *= -1;
          }
        }
        sort(cells.begin(), cells.end(), cmp1);
        cells2 = cells;
        sort(cells2.begin(), cells2.end(), cmp2);
        vector<int> ord = {1, 2, 3};
        upd(invx, invy, ord, bestK, cells, cells2);
        while (next_permutation(ord.begin(), ord.end())) {
          upd(invx, invy, ord, bestK, cells, cells2);
        }
        if (invx) {
          for (auto &cell : cells) {
            cell.x *= -1;
          }
        }
        if (invy) {
          for (auto &cell : cells) {
            cell.y *= -1;
          }
        }
      }
    }
    for (auto &cell : cells) {
      swap(cell.x, cell.y);
    }
  }
  cout << 3 * bestK << "\n";
}

### Prompt

Your challenge is to write a Cpp solution 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;
bool home = true;
struct Cell {
  int x;
  int y;
  int type;
};
bool cmp1(Cell a, Cell b) { return a.x < b.x; }
bool cmp2(Cell a, Cell b) { return a.y < b.y; }
const int N = (int)1e5 + 7;
int n;
bool okLR(vector<Cell> &cells, int need, vector<int> ord) {
  int first = ord[0], second = ord[1], third = ord[2];
  int cntFirst = 0;
  for (int i = 0; i < n; i++) {
    if (cells[i].type == first) {
      cntFirst++;
      if (cntFirst == need) {
        int cntSecond = 0;
        for (int j = i + 1; j < n; j++) {
          if (cells[j].x > cells[i].x && cells[j].type == second) {
            cntSecond++;
            if (cntSecond == need) {
              int cntThird = 0;
              for (int k = j + 1; k < n; k++) {
                if (cells[k].x > cells[j].x && cells[k].type == third) {
                  cntThird++;
                  if (cntThird == need) {
                    return true;
                  }
                }
              }
              return false;
            }
          }
        }
        return false;
      }
    }
  }
  assert(false);
}
struct Bbox {
  int xmin = (int)1e9, ymin = (int)1e9;
  int xmax = -(int)1e9, ymax = -(int)1e9;
  int ind;
  void add(int x, int y) {
    xmin = min(xmin, x);
    xmax = max(xmax, x);
    ymin = min(ymin, y);
    ymax = max(ymax, y);
  }
};
bool okUD(vector<Cell> &cells, vector<Cell> &cells2, int need,
          vector<int> ord) {
  int first = ord[0], second = ord[1], third = ord[2];
  int cntFirst = 0;
  for (int i = 0; i < n; i++) {
    if (cells[i].type == first) {
      cntFirst++;
      if (cntFirst == need) {
        int cntSecond = 0;
        for (int j = 0; j < n; j++) {
          if (cells2[j].x > cells[i].x && cells2[j].type == second) {
            cntSecond++;
            if (cntSecond == need) {
              int cntThird = 0;
              for (int k = j + 1; k < n; k++) {
                if (cells2[k].y > cells2[j].y && cells2[k].x > cells[i].x &&
                    cells2[k].type == third) {
                  cntThird++;
                  if (cntThird == need) {
                    return true;
                  }
                }
              }
              return false;
            }
          }
        }
        return false;
      }
    }
  }
  assert(false);
}
void upd(int invx, int invy, vector<int> ord, int &bestK, vector<Cell> cells,
         vector<Cell> cells2) {
  int low = bestK + 1, high = n / 3;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (okLR(cells, mid, ord)) {
      bestK = mid;
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
  low = bestK + 1;
  high = n / 3;
  while (low <= high) {
    int mid = (low + high) / 2;
    if (okUD(cells, cells2, mid, ord)) {
      bestK = mid;
      low = mid + 1;
    } else {
      high = mid - 1;
    }
  }
}
signed main() {
  if (!home) {
    ios::sync_with_stdio(0);
    cin.tie(0);
  }
  cin >> n;
  vector<Cell> cells(n);
  for (auto &cell : cells) {
    cin >> cell.x >> cell.y >> cell.type;
  }
  int bestK = 0;
  for (int swp = 0; swp < 2; swp++) {
    for (int invx = 0; invx < 2; invx++) {
      for (int invy = 0; invy < 2; invy++) {
        vector<Cell> cells2;
        if (invx) {
          for (auto &cell : cells) {
            cell.x *= -1;
          }
        }
        if (invy) {
          for (auto &cell : cells) {
            cell.y *= -1;
          }
        }
        sort(cells.begin(), cells.end(), cmp1);
        cells2 = cells;
        sort(cells2.begin(), cells2.end(), cmp2);
        vector<int> ord = {1, 2, 3};
        upd(invx, invy, ord, bestK, cells, cells2);
        while (next_permutation(ord.begin(), ord.end())) {
          upd(invx, invy, ord, bestK, cells, cells2);
        }
        if (invx) {
          for (auto &cell : cells) {
            cell.x *= -1;
          }
        }
        if (invy) {
          for (auto &cell : cells) {
            cell.y *= -1;
          }
        }
      }
    }
    for (auto &cell : cells) {
      swap(cell.x, cell.y);
    }
  }
  cout << 3 * bestK << "\n";
}

```