write a go solution for G. X Auratime limit per test1 secondmemory limit per test1024 megabytesinputstandard inputoutputstandard outputMount ICPC can be represented as a grid of R rows (numbered from 1 to R) and C columns (numbered from 1 to C). The cell located at row r and column c is denoted as (r,c) and has a height of H_r,c. Two cells are adjacent to each other if they share a side. Formally, (r,c) is adjacent to (r-1,c), (r+1,c), (r,c-1), and (r,c+1), if any exists.You can move only between adjacent cells, and each move comes with a penalty. With an aura of an odd positive integer X, moving from a cell with height h_1 to a cell with height h_2 gives you a penalty of (h_1-h_2)^X. Note that the penalty can be negative.You want to answer Q independent scenarios. In each scenario, you start at the starting cell (R_s,C_s) and you want to go to the destination cell (R_f,C_f) with minimum total penalty. In some scenarios, the total penalty might become arbitrarily small; such a scenario is called invalid. Find the minimum total penalty to move from the starting cell to the destination cell, or determine if the scenario is invalid.InputThe first line consists of three integers R C X (1<=R,C<=1000;1<=X<=9;X is an odd integer).Each of the next R lines consists of a string H_r of length C. Each character in H_r is a number from 0 to 9. The c-th character of H_r represents the height of cell (r,c), or H_r,c.The next line consists of an integer Q (1<=Q<=100,000).Each of the next Q lines consists of four integers R_s C_s R_f C_f (1<=R_s,R_f<=R;1<=C_s,C_f<=C).OutputFor each scenario, output the following in a single line. If the scenario is invalid, output INVALID. Otherwise, output a single integer representing the minimum total penalty to move from the starting cell to the destination cell.ExamplesInput3 4 1
3359
4294
3681
5
1 1 3 4
3 3 2 1
2 2 1 4
1 3 3 2
1 1 1 1
Output2
4
-7
-1
0
Input2 4 5
1908
2023
2
1 1 2 4
1 1 1 1
OutputINVALID
INVALID
Input3 3 9
135
357
579
2
3 3 1 1
2 2 2 2
Output2048
0
NoteExplanation for the sample input/output #1For the first scenario, one of the solutions is to move as follows: (1,1)arrow(2,1)arrow(3,1)arrow(3,2)arrow(3,3)arrow(3,4). The total penalty of this solution is (3-4)^1+(4-3)^1+(3-6)^1+(6-8)^1+(8-1)^1=2.Explanation for the sample input/output #2For the first scenario, the cycle (1,1)arrow(2,1)arrow(2,2)arrow(1,2)arrow(1,1) has a penalty of (1-2)^5+(2-0)^5+(0-9)^5+(9-1)^5=-26250. You can keep repeating this cycle to make your total penalty arbitrarily small. Similarly, for the second scenario, you can move to (1,1) first, then repeat the same cycle.. Output only the code with no comments, explanation, or additional text.