103663: [Atcoder]ABC366 D - Cuboid Sum Query

Problem Statement

You are given a positive integer $N$, and an integer $A_{x,y,z}$ for each triple of integers $(x, y, z)$ such that $1 \leq x, y, z \leq N$.

You will be given $Q$ queries in the following format, which must be processed in order.

For the $i$-th query $(1 \leq i \leq Q)$, you are given a tuple of integers $(Lx_i, Rx_i, Ly_i, Ry_i, Lz_i, Rz_i)$ such that $1 \leq Lx_i \leq Rx_i \leq N$, $1 \leq Ly_i \leq Ry_i \leq N$, and $1 \leq Lz_i \leq Rz_i \leq N$. Find:

$\displaystyle{\sum_{x=Lx_i}^{Rx_i} \sum_{y=Ly_i}^{Ry_i} \sum_{z=Lz_i}^{Rz_i} A_{x,y,z}}$.

Constraints

• $1 \leq N \leq 100$
• $1 \leq Q \leq 2 \times 10^{5}$
• $0 \leq A_{x,y,z} \leq 999$ $(1 \leq x, y, z \leq N)$
• $1 \leq Lx_i \leq Rx_i \leq N$ $(1 \leq i \leq Q)$
• $1 \leq Ly_i \leq Ry_i \leq N$ $(1 \leq i \leq Q)$
• $1 \leq Lz_i \leq Rz_i \leq N$ $(1 \leq i \leq Q)$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$
$A_{1,1,1}$ $A_{1,1,2}$ $\ldots$ $A_{1,1,N}$
$A_{1,2,1}$ $A_{1,2,2}$ $\ldots$ $A_{1,2,N}$
$\vdots$
$A_{1,N,1}$ $A_{1,N,2}$ $\ldots$ $A_{1,N,N}$
$A_{2,1,1}$ $A_{2,1,2}$ $\ldots$ $A_{2,1,N}$
$A_{2,2,1}$ $A_{2,2,2}$ $\ldots$ $A_{2,2,N}$
$\vdots$
$A_{2,N,1}$ $A_{2,N,2}$ $\ldots$ $A_{2,N,N}$
$\vdots$
$A_{N,1,1}$ $A_{N,1,2}$ $\ldots$ $A_{N,1,N}$
$A_{N,2,1}$ $A_{N,2,2}$ $\ldots$ $A_{N,2,N}$
$\vdots$
$A_{N,N,1}$ $A_{N,N,2}$ $\ldots$ $A_{N,N,N}$
$Q$
$Lx_1$ $Rx_1$ $Ly_1$ $Ry_1$ $Lz_1$ $Rz_1$
$Lx_2$ $Rx_2$ $Ly_2$ $Ry_2$ $Lz_2$ $Rz_2$
$\vdots$
$Lx_Q$ $Rx_Q$ $Ly_Q$ $Ry_Q$ $Lz_Q$ $Rz_Q$

Output

Print $Q$ lines. The $i$-th line should contain the answer to the $i$-th query.

Sample Input 1

2
1 2
3 4
5 6
7 8
2
1 2 2 2 1 1
2 2 1 2 1 2

Sample Output 1

10
26

For the 1st query, the sought value is $A_{1,2,1} + A_{2,2,1} = 3 + 7 = 10$. Thus, print $10$.

For the 2nd query, the sought value is $A_{2,1,1} + A_{2,1,2} + A_{2,2,1} + A_{2,2,2} = 5 + 6 + 7 + 8 = 26$. Thus, print $26$.

Sample Input 2

3
733 857 714
956 208 257
123 719 648
840 881 245
245 112 746
306 942 694
58 870 849
13 208 789
687 906 783
8
3 3 3 3 1 1
1 3 2 3 3 3
2 2 2 3 1 1
1 3 1 1 1 1
2 3 2 3 2 3
1 2 1 1 1 2
3 3 2 2 1 3
1 2 2 3 2 3

Sample Output 2

687
3917
551
1631
5180
3311
1010
4326