835_C. Star sky
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.
```python
import sys
from bisect import bisect_left, bisect_right

n, q, c = list(map(int, input().split()))

values = [[[0 for _ in range(11)] for _ in range(0, 101)] for _ in range(0, 101)]
# print(dp)
for i in range(n):
    x, y, s = list(map(int, sys.stdin.readline().split()))

    values[x][y][s] += 1


dp = [[[-1 for _ in range(11)] for _ in range(0, 101)] for _ in range(0, 101)]
for i in range(0,101):
    for p in range(11):
        dp[0][i][p]=0
        dp[i][0][p]=0
def recurse(p, x, y):
    if x==0 or y==0:
        return 0
    if dp[x][y][p]!=-1:
        return dp[x][y][p]
    if x == 1 and y == 1:
        dp[x][y][p]=values[x][y][p]
        return values[x][y][p]
    else:
        # print(x,y,p)

        dp[x][y][p]=recurse(p,x-1,y)+recurse(p,x,y-1)-recurse(p,x-1,y-1)+values[x][y][p]
        dp[x][y][p]=max(dp[x][y][p],0)

        return dp[x][y][p]
for i in range(1,101):
    for j in range(1,101):
        for p in range(0,c+1):
            recurse(p,i,j)
# print(dp)
for i in range(q):
    t,x1,y1,x2,y2=list(map(int, sys.stdin.readline().split()))
    ans=0
    for k in range(0,c+1):
        # print(dp[x2][y2][k])
        # print(dp[x1-1][y2][k])
        # print(dp[x1][y2-1][k])
        # print(dp[x1-1][y1-1][k])
        ans+=((t+k)%(c+1))*(dp[x2][y2][k]-dp[x1-1][y2][k]-dp[x2][y1-1][k]+dp[x1-1][y1-1][k])
    print(ans)

```