#include <cassert>
#include <cmath>
#include <algorithm>
#include <float.h>
#include <iostream>
#include <iomanip>
#include <limits.h>
#include <map>
#include <queue>
#include <set>
#include <string.h>
#include <vector>

using namespace std;
typedef long long ll;

struct Point {
  double x;
  double y;
  char d;

  Point(double x = -1, double y = -1, char d = 'U') {
    this->x = x;
    this->y = y;
    this->d = d;
  }
};

vector<Point> points;
int N;

double f(double t) {
  double max_y = -10000000000;
  double max_x = -10000000000;
  double min_y = 10000000000;
  double min_x = 10000000000;

  for (int i = 0; i < N; ++i) {
    Point p = points[i];

    switch(p.d) {
      case 'U':
        p.y += t;
        break;
      case 'D':
        p.y -= t;
        break;
      case 'L':
        p.x -= t;
        break;
      case 'R':
        p.x += t;
        break;
    }

    min_y = min(min_y, p.y);
    min_x = min(min_x, p.x);
    max_y = max(max_y, p.y);
    max_x = max(max_x, p.x);
  }

  return (max_y - min_y) * (max_x - min_x);
}

int main() {
  cin >> N;

  double x, y;
  char d;

  for (int i = 0; i < N; ++i) {
    cin >> x >> y >> d;
    points.push_back(Point(x, y, d));
  }

  double left = 0.0;
  double right = 100000000;

  for (int i = 0; i < 200; ++i) {
    double t1 = (left * 2 + right) / 3.0;
    double t2 = (left + right * 2) / 3.0;

    if (f(t1) < f(t2)) {
      right = t2;
    } else {
      left = t1;
    }
  }

  double time = (left + right) / 2.0;
  cout << fixed << setprecision(12) << f(time) << endl;

  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

There are N points in a two-dimensional plane. The initial coordinates of the i-th point are (x_i, y_i). Now, each point starts moving at a speed of 1 per second, in a direction parallel to the x- or y- axis. You are given a character d_i that represents the specific direction in which the i-th point moves, as follows:

* If d_i = `R`, the i-th point moves in the positive x direction;
* If d_i = `L`, the i-th point moves in the negative x direction;
* If d_i = `U`, the i-th point moves in the positive y direction;
* If d_i = `D`, the i-th point moves in the negative y direction.



You can stop all the points at some moment of your choice after they start moving (including the moment they start moving). Then, let x_{max} and x_{min} be the maximum and minimum among the x-coordinates of the N points, respectively. Similarly, let y_{max} and y_{min} be the maximum and minimum among the y-coordinates of the N points, respectively.

Find the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}) and print it.

Constraints

* 1 \leq N \leq 10^5
* -10^8 \leq x_i,\ y_i \leq 10^8
* x_i and y_i are integers.
* d_i is `R`, `L`, `U`, or `D`.

Input

Input is given from Standard Input in the following format:


N
x_1 y_1 d_1
x_2 y_2 d_2
.
.
.
x_N y_N d_N


Output

Print the minimum possible value of (x_{max} - x_{min}) \times (y_{max} - y_{min}).

The output will be considered correct when its absolute or relative error from the judge's output is at most 10^{-9}.

Examples

Input

2
0 3 D
3 0 L


Output

0


Input

5
-7 -10 U
7 -6 U
-8 7 D
-3 3 D
0 -6 R


Output

97.5


Input

20
6 -10 R
-4 -9 U
9 6 D
-3 -2 R
0 7 D
4 5 D
10 -10 U
-1 -8 U
10 -6 D
8 -5 U
6 4 D
0 3 D
7 9 R
9 -4 R
3 10 D
1 9 U
1 -6 U
9 -8 R
6 7 D
7 -3 D


Output

273

### Response

```cpp
#include <cassert>
#include <cmath>
#include <algorithm>
#include <float.h>
#include <iostream>
#include <iomanip>
#include <limits.h>
#include <map>
#include <queue>
#include <set>
#include <string.h>
#include <vector>

using namespace std;
typedef long long ll;

struct Point {
  double x;
  double y;
  char d;

  Point(double x = -1, double y = -1, char d = 'U') {
    this->x = x;
    this->y = y;
    this->d = d;
  }
};

vector<Point> points;
int N;

double f(double t) {
  double max_y = -10000000000;
  double max_x = -10000000000;
  double min_y = 10000000000;
  double min_x = 10000000000;

  for (int i = 0; i < N; ++i) {
    Point p = points[i];

    switch(p.d) {
      case 'U':
        p.y += t;
        break;
      case 'D':
        p.y -= t;
        break;
      case 'L':
        p.x -= t;
        break;
      case 'R':
        p.x += t;
        break;
    }

    min_y = min(min_y, p.y);
    min_x = min(min_x, p.x);
    max_y = max(max_y, p.y);
    max_x = max(max_x, p.x);
  }

  return (max_y - min_y) * (max_x - min_x);
}

int main() {
  cin >> N;

  double x, y;
  char d;

  for (int i = 0; i < N; ++i) {
    cin >> x >> y >> d;
    points.push_back(Point(x, y, d));
  }

  double left = 0.0;
  double right = 100000000;

  for (int i = 0; i < 200; ++i) {
    double t1 = (left * 2 + right) / 3.0;
    double t2 = (left + right * 2) / 3.0;

    if (f(t1) < f(t2)) {
      right = t2;
    } else {
      left = t1;
    }
  }

  double time = (left + right) / 2.0;
  cout << fixed << setprecision(12) << f(time) << endl;

  return 0;
}

```