C. Star sky
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

Over time the stars twinkle. At moment 0 the i-th star has brightness s i. 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 t i and you will see a rectangle with sides parallel to the coordinate axes, the lower left corner has coordinates ( x 1i, y 1i) and the upper right — ( x 2i, y 2i). 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 x i, y i, s i (1 ≤ x i, y i ≤ 100, 0 ≤ s i ≤ 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 t i, x 1i, y 1i, x 2i, y 2i (0 ≤ t i ≤ 109, 1 ≤ x 1i < x 2i ≤ 100, 1 ≤ y 1i < y 2i ≤ 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 31 1 13 2 02 1 1 2 20 2 1 4 55 1 1 5 5
Output
303
Input
3 4 51 1 22 3 03 3 10 1 1 100 1001 2 2 4 42 2 1 4 71 50 50 51 51
Output
3350
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.