The Cartesian coordinate system is set in the sky. There you can see n stars, the i-th has coordinates (xi, yi), a maximum brightness c, equal for all stars, and an initial brightness si (0 ≤ si ≤ c).

Over time the stars twinkle. At moment 0 the i-th star has brightness si. Let at moment t some star has brightness x. Then at moment (t + 1) this star will have brightness x + 1, if x + 1 ≤ c, and 0, otherwise.

You want to look at the sky q times. In the i-th time you will look at the moment ti and you will see a rectangle with sides parallel to the coordinate axes, the lower left corner has coordinates (x1i, y1i) and the upper right — (x2i, y2i). For each view, you want to know the total brightness of the stars lying in the viewed rectangle.

A star lies in a rectangle if it lies on its border or lies strictly inside it.

Input

The first line contains three integers n, q, c (1 ≤ n, q ≤ 105, 1 ≤ c ≤ 10) — the number of the stars, the number of the views and the maximum brightness of the stars.

The next n lines contain the stars description. The i-th from these lines contains three integers xi, yi, si (1 ≤ xi, yi ≤ 100, 0 ≤ si ≤ c ≤ 10) — the coordinates of i-th star and its initial brightness.

The next q lines contain the views description. The i-th from these lines contains five integers ti, x1i, y1i, x2i, y2i (0 ≤ ti ≤ 109, 1 ≤ x1i < x2i ≤ 100, 1 ≤ y1i < y2i ≤ 100) — the moment of the i-th view and the coordinates of the viewed rectangle.

Output

For each view print the total brightness of the viewed stars.

Examples

Input

2 3 3
1 1 1
3 2 0
2 1 1 2 2
0 2 1 4 5
5 1 1 5 5


Output

3
0
3


Input

3 4 5
1 1 2
2 3 0
3 3 1
0 1 1 100 100
1 2 2 4 4
2 2 1 4 7
1 50 50 51 51


Output

3
3
5
0

Note

Let's consider the first example.

At the first view, you can see only the first star. At moment 2 its brightness is 3, so the answer is 3.

At the second view, you can see only the second star. At moment 0 its brightness is 0, so the answer is 0.

At the third view, you can see both stars. At moment 5 brightness of the first is 2, and brightness of the second is 1, so the answer is 3.
import java.util.Scanner;
public class C{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int q = sc.nextInt();
        int c = sc.nextInt();
        int [][][] stars = new int[100][100][c+1];
        int x = 0, y = 0, si = 0;
        for(int i = 0; i < n; i++){
            x = sc.nextInt();
            y = sc.nextInt();
            si = sc.nextInt();
            stars[x-1][y-1][si]++;
        }

        int [][][] sum = new int[100][100][c+1];
        int currentSum = 0;
        for(int i = 0; i < c+1; i++){
            for(int j = 0; j < 100; j++){
                for(int k = 0; k < 100; k++){
                    currentSum = 0;
                    currentSum += stars[j][k][i];                    
                    if(k-1 >= 0){
                        currentSum += sum[j][k-1][i];
                    }
                    if(j-1 >= 0){
                        currentSum += sum[j-1][k][i];
                    }
                    if(j-1 >= 0 && k-1 >= 0){
                        currentSum -= sum[j-1][k-1][i];
                    }
                    sum[j][k][i] = currentSum;
                }
            }
        }
        int result = 0;
        int total = 0;
        for(int i = 0; i < q; i++){
            
            int t = sc.nextInt();
            int x1 = sc.nextInt()-1;
            int y1 = sc.nextInt()-1;
            int x2 = sc.nextInt()-1;
            int y2 = sc.nextInt()-1;
            int state = 0;
            for(int m = 0; m < c+1; m++){
                result  = 0;
                state = (t + m)%(c+1);
                result += sum[x2][y2][m];
                if(x1-1 >= 0){
                    result -= sum[x1-1][y2][m];
                }
                if(y1-1 >= 0){
                    result -= sum[x2][y1-1][m];
                }
                if(x1-1 >= 0 && y1-1 >= 0){
                    result += sum[x1-1][y1-1][m];
                }
                total += result * state;
            }
            
            System.out.println(total);
            total = 0;
        }
        /*
        for(int i = 0; i < c+1; i++) {
            for(int j = 0; j < 3; j++){
                for(int k = 0; k < 3; k++){
                    System.out.print(stars[k][j][i]+" ");
                }
                System.out.println();
            }
            System.out.println("---------");
        }
        int threshold = 5;
        for(int i = 0; i < c+1; i++) {
            for(int j = 0; j < threshold; j++){
                for(int k = 0; k < threshold; k++){
                    System.out.print(sum[k][j][i]+ " ");
                }
                System.out.println();
            }
            System.out.println("---------");
        }
        */
        sc.close();
    }
}