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.io.*;
import java.util.StringTokenizer;

public class Main {

    private static void initOneRow(int x1, int y1, int s1, int[][][] starBrihtnessOverTime, int c) {
        for(int i = 0; i <= c; i++){
            starBrihtnessOverTime[i][x1][y1] += (i + s1) % (c + 1);
        }
    }


    public static void main(String[] args) {
        ManualReader in = getManualReader();
        int n = in.nextInt();
        int q = in.nextInt();
        int c = in.nextInt();

        int [][][] starBrihtnessOverTime = new int [c+1][101][101];
        for(int j = 0; j < n; j ++){
            int x1 = in.nextInt();
            int y1 = in.nextInt();
            int s1 = in.nextInt();
            initOneRow(x1, y1, s1, starBrihtnessOverTime, c);
        }
        for(int i=0;i<=c;i++) {
            for(int j=1;j<101;j++)
                for(int k=1;k<101;k++)
                    starBrihtnessOverTime[i][j][k]+= starBrihtnessOverTime[i][j-1][k] + starBrihtnessOverTime[i][j][k-1] - starBrihtnessOverTime[i][j-1][k-1];
        }

        for(int i = 0; i < q; i++){
            int t1 = in.nextInt();
            int x1 = in.nextInt();
            int y1 = in.nextInt();
            int x2 = in.nextInt();
            int y2 = in.nextInt();
            int t = t1 % (c + 1);
            System.out.println(starBrihtnessOverTime[t][x1-1][y1-1]+starBrihtnessOverTime[t][x2][y2]-starBrihtnessOverTime[t][x2][y1-1]-starBrihtnessOverTime[t][x1-1][y2]);
        }
    }

    private static ManualReader getManualReader(){
        InputStreamReader inputStream = new InputStreamReader(System.in);
        BufferedReader reader = new BufferedReader(inputStream);
        ManualReader in = new ManualReader(reader);
        return in;
    }

    static class ManualReader{
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        public ManualReader(BufferedReader reader){
            this.reader = reader;
            tokenizer = null;
        }

        public String nextLine() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextLine());
        }

        public long nextLong() {
            return Long.parseLong(nextLine());
        }
    }
}