# Untitled

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```Kim is trekking in the Jeju islands. He wants to get to his destination with the lowest amount of energy used. However, he does not want to spend more time to save energy. Fortunately Kim has a map.

Map is NxN with values equal to the land height.

He cannot move diagonally. It takes the same time to move one cell, independent of height.
If he moves the same height or smaller than the current, energy of 1 is used.
When moving to a position with height greater than the current position, energy of (height difference + 1) is used.

Starting point (1,1) & destination (N,N) are fixed.

Among several paths moving within the minimum time, find the path which uses the least energy. Write a solution which prints energy for that path.

Constraints:
4<=N<= 12
0<=Height<=9
Cannot move diagonally
Example
input
4
9 5 7 9
8 4 2 5
7 6 5 4
8 8 9 5

output
7

3 sample examples provided

50
4
9 5 7 9
8 4 2 5
7 6 5 4
8 8 9 5
6
3 2 6 0 1 2
9 2 2 9 2 9
4 9 2 2 0 1
0 2 4 2 2 4
4 5 0 1 2 2
9 8 1 7 5 1
8
1 1 1 1 1 1 1 1
9 9 9 9 9 9 9 1
9 9 9 9 9 9 9 1
9 9 9 9 1 1 1 1
9 9 9 9 1 9 9 9
9 9 9 9 1 9 9 9
9 9 9 9 1 9 9 9
9 9 9 9 1 1 1 1
4
9 8 2 9
2 4 5 8
9 2 9 0
1 0 5 2
11
8 2 6 5 1 5 3 6 7 4 4
6 3 7 6 5 8 6 4 5 4 8
6 5 5 5 5 3 9 7 5 3 3
3 4 5 8 9 9 5 8 9 0 1
7 6 7 2 0 6 9 4 8 5 9
3 4 5 1 1 1 1 9 1 7 3
7 5 0 7 6 8 6 5 9 5 5
2 6 6 4 3 0 9 6 4 5 0
1 9 8 5 6 8 1 2 7 8 6
2 7 6 1 3 9 1 7 9 3 7
2 8 4 7 3 3 4 2 3 4 0
8
9 4 3 1 9 6 5 5
4 5 4 6 7 5 4 8
4 1 7 7 2 0 5 3
3 2 3 4 1 4 1 6
0 1 5 2 8 1 9 8
4 5 4 8 3 8 3 5
8 8 0 2 9 8 4 2
1 7 4 7 8 8 5 0
7
8 0 8 2 9 6 9
6 5 7 5 0 4 8
3 1 6 1 2 6 0
1 9 5 7 0 1 8
9 4 0 2 9 1 2
8 2 4 3 9 6 7
4 7 7 0 9 5 2
4
9 0 1 9
8 4 7 5
1 4 6 6
0 7 5 2
10
0 3 3 6 8 4 2 8 3 9
2 9 6 1 9 7 9 3 6 1
5 2 3 2 2 3 1 6 2 8
6 3 7 0 3 6 7 8 0 1
6 6 4 7 2 7 0 8 1 9
6 0 2 9 1 6 3 9 0 8
6 5 6 6 9 5 6 2 3 3
7 3 8 5 8 4 3 9 9 0
9 8 8 4 6 2 0 8 8 3
2 5 5 7 4 1 9 2 2 6
8
9 0 5 6 4 9 8 4
2 6 7 9 1 6 3 5
8 1 5 8 7 7 2 2
4 5 9 2 5 6 4 9
4 6 4 8 9 0 2 2
9 4 3 1 7 3 1 2
2 4 7 4 1 6 5 3
9 7 1 1 6 6 0 4
12
3 1 9 3 1 2 7 9 9 4 8 4
1 5 3 4 1 5 1 2 9 2 4 3
0 1 9 8 0 5 0 2 3 7 7 3
8 4 2 8 0 8 2 3 0 9 7 5
7 8 2 3 2 3 2 9 9 0 3 3
4 9 3 6 4 2 5 9 4 7 5 3
8 9 2 8 1 9 0 3 9 6 2 8
6 8 7 2 3 7 4 7 9 8 7 8
2 4 1 0 7 1 3 6 3 6 7 3
1 5 4 3 3 8 2 0 4 4 0 9
3 4 2 4 0 1 0 0 3 4 8 6
9 8 0 3 4 7 6 0 8 2 1 5
9
1 7 7 8 3 4 3 3 0
2 8 3 8 0 5 0 3 9
1 9 4 7 9 9 6 7 4
4 5 1 3 6 9 0 2 8
4 1 0 5 0 6 0 9 3
3 0 1 4 5 6 6 9 2
5 7 8 0 1 4 3 0 8
3 7 9 1 3 1 5 5 6
1 1 6 2 7 1 6 7 8
5
3 2 8 7 1
7 8 4 7 6
6 0 2 0 2
5 3 5 6 0
7 3 7 6 4
11
8 0 0 1 1 2 9 3 8 4 4
9 5 0 0 5 7 7 6 2 9 8
9 8 2 2 6 3 3 8 2 6 0
8 7 1 6 9 5 8 7 7 9 5
9 5 4 9 7 6 0 0 8 9 3
1 1 3 7 0 6 1 2 6 4 2
2 6 0 9 6 5 1 2 7 8 4
8 0 0 4 9 6 6 7 0 7 9
7 1 0 2 2 8 1 9 8 8 7
4 1 3 1 8 0 3 9 9 4 1
1 9 6 5 9 0 0 8 8 2 0
5
1 8 8 6 7
8 4 5 3 5
6 8 8 6 8
0 0 4 4 6
3 7 4 8 9
5
8 0 6 6 0
4 6 0 9 6
2 0 7 3 3
3 0 5 8 4
6 4 2 0 2
10
5 8 6 0 7 0 7 7 5 3
4 8 5 9 4 5 4 4 3 3
5 6 5 4 5 4 8 7 8 1
7 2 8 6 4 2 1 3 1 4
3 4 3 3 1 0 3 4 5 1
4 3 0 0 2 0 9 0 0 2
7 6 9 1 0 8 6 6 4 9
9 2 6 2 3 7 2 1 2 8
8 3 9 8 2 6 2 9 0 5
1 3 8 8 3 5 0 6 6 2
6
4 6 0 6 9 6
5 7 9 8 6 5
0 5 3 5 3 5
0 9 5 9 2 8
3 0 7 5 9 5
8 2 5 5 9 7
11
2 7 5 2 8 1 4 8 5 2 2
6 2 5 2 1 2 0 1 1 2 6
3 3 5 5 8 9 5 4 0 1 3
2 5 1 9 0 3 3 2 6 6 9
4 9 6 7 5 7 8 5 4 7 6
8 6 0 2 2 0 6 9 8 2 0
8 1 8 0 6 7 1 2 3 8 1
7 2 3 9 2 8 4 1 2 6 3
3 5 5 6 9 0 8 2 4 4 8
4 5 0 9 6 5 4 5 2 0 2
7 4 3 4 4 2 6 5 3 4 9
8
0 2 7 4 2 5 4 0
0 4 5 1 8 3 5 6
6 9 8 8 6 7 5 3
7 8 9 9 8 6 8 7
6 7 8 9 8 9 8 2
1 0 1 5 6 8 7 1
1 2 7 3 9 4 0 7
9 9 7 5 7 2 3 6
12
9 8 7 8 9 8 2 6 1 7 5 7
1 1 4 7 0 6 4 7 7 3 4 9
1 9 8 6 5 3 2 6 7 8 9 1
8 0 2 4 5 2 7 1 5 9 5 8
7 4 8 8 9 2 6 8 8 1 1 3
0 7 2 3 5 4 5 9 8 5 2 4
5 7 0 5 8 3 2 0 2 2 9 8
4 4 9 5 1 6 9 1 4 5 0 8
2 8 8 6 9 4 4 6 5 6 0 3
2 0 1 1 9 1 9 3 8 4 5 5
7 7 7 2 1 5 1 7 1 0 4 3
0 0 4 3 0 6 2 4 8 0 7 0
12
9 5 0 6 9 6 0 6 0 3 5 3
5 8 7 2 9 7 6 5 7 0 0 5
8 1 6 9 3 0 6 8 6 0 5 9
1 4 1 5 2 1 7 2 8 7 8 8
0 0 5 0 5 4 7 0 6 4 5 6
0 1 1 9 3 1 8 5 6 6 9 0
8 2 3 8 8 5 8 1 6 9 2 2
2 5 4 0 7 2 3 0 1 8 1 1
1 0 3 4 6 4 5 4 8 2 2 7
5 0 3 9 9 2 1 4 6 9 6 7
4 2 1 7 3 2 3 0 9 2 4 3
6 5 2 6 3 4 4 5 0 6 1 2
10
9 0 2 4 9 1 1 1 1 7
5 6 5 3 5 5 5 6 5 1
9 5 4 6 6 0 9 1 9 9
6 4 2 3 4 5 1 4 9 3
6 0 2 6 5 4 0 4 2 1
5 0 7 9 6 7 3 2 9 8
1 1 3 8 2 5 7 2 4 8
4 1 4 2 4 2 4 7 5 1
3 7 2 1 3 2 3 7 9 0
1 9 6 6 2 4 7 8 4 3
12
3 9 3 6 5 4 0 2 8 9 6 5
0 5 7 1 3 0 1 3 6 6 3 6
7 2 6 3 4 1 4 4 0 8 0 5
0 2 4 7 4 1 4 7 2 8 5 8
1 7 8 8 1 1 7 9 7 2 8 3
7 8 3 7 9 5 1 1 9 6 6 3
8 8 0 4 7 3 5 6 6 1 9 9
5 8 0 7 1 8 4 0 2 4 7 5
2 9 1 3 6 5 2 4 9 2 3 9
1 4 1 8 3 6 2 1 2 1 8 4
1 8 1 1 9 5 9 6 3 9 1 9
9 2 5 6 4 3 5 1 9 1 1 4
11
9 1 3 6 6 2 2 0 0 6 0
6 3 8 0 8 8 9 4 4 7 0
1 8 0 1 9 1 0 5 0 9 3
7 8 3 8 9 7 1 5 9 0 5
1 4 5 2 4 3 6 5 2 0 1
8 6 0 2 5 5 2 2 4 6 3
7 2 8 5 5 3 0 9 4 0 4
3 5 5 9 8 2 8 6 5 3 0
0 2 7 2 1 0 2 5 3 2 1
9 2 0 8 3 2 8 5 6 0 5
0 8 6 1 9 2 9 1 1 1 8
5
5 5 8 0 7
3 4 4 9 1
4 7 1 9 4
5 1 2 7 1
9 8 3 5 0
11
1 6 8 2 0 1 5 0 2 8 9
2 5 2 4 5 3 5 6 6 0 7
4 6 3 7 9 2 3 1 3 5 9
0 6 9 5 3 1 2 4 0 3 3
0 1 4 4 3 5 8 6 2 3 5
9 9 9 4 1 1 9 4 7 6 7
0 5 6 1 4 1 3 3 5 5 1
1 4 5 8 2 6 3 4 0 3 8
6 2 7 7 7 9 8 6 6 3 8
8 9 2 0 0 7 1 1 5 2 1
6 8 8 7 0 3 1 6 1 9 4
8
5 1 4 6 0 8 1 9
2 8 2 2 0 9 8 2
2 8 2 0 9 8 3 5
7 6 8 7 8 3 1 5
6 6 8 6 2 6 0 9
8 4 6 8 8 9 2 2
0 8 4 1 5 1 3 8
2 1 4 4 5 5 2 0
7
1 2 7 2 0 9 9
1 7 4 1 7 1 2
4 0 4 4 8 3 9
8 4 3 0 3 4 3
3 6 1 2 5 1 5
7 8 5 4 2 1 4
7 8 1 9 4 5 1
7
8 4 8 4 0 4 6
3 2 4 7 1 4 7
8 1 1 4 9 5 2
3 4 5 7 2 1 7
0 3 2 4 4 1 2
9 6 5 0 3 5 8
5 1 6 6 5 8 0
5
9 2 7 2 0
6 0 7 6 4
1 7 8 6 6
9 8 9 5 4
6 0 9 2 5
4
1 5 5 9
7 9 3 5
8 0 8 9
0 3 1 3
7
0 3 4 7 1 2 0
1 9 3 5 5 0 2
3 1 6 7 9 2 0
4 7 5 4 1 6 0
1 0 8 2 8 0 5
5 2 4 9 2 8 8
8 4 9 0 7 2 5
11
6 2 7 7 5 6 6 7 8 7 2
4 7 7 5 0 2 9 5 0 6 7
8 8 3 4 1 5 6 2 6 6 9
4 9 1 2 2 2 8 2 0 2 6
6 4 7 2 3 6 1 1 9 4 8
0 5 8 1 9 4 2 9 8 4 2
2 4 5 5 4 6 0 9 7 0 1
7 6 9 8 2 5 7 3 3 2 5
9 1 7 1 8 5 2 9 8 7 7
1 8 3 3 4 1 9 0 5 8 7
1 2 3 3 6 0 1 2 3 4 7
7
8 5 6 3 9 4 6
4 9 8 8 1 3 1
2 1 2 1 0 4 7
0 4 0 1 0 5 3
5 1 7 5 1 8 6
8 8 8 0 7 7 1
9 7 3 7 7 9 8
7
5 8 4 9 5 1 5
5 5 1 9 1 6 8
5 9 8 2 9 4 5
7 2 2 3 3 9 6
2 4 2 4 5 9 7
7 9 2 8 3 6 1
5 5 9 4 5 7 2
11
7 5 3 7 7 6 7 3 4 9 2
1 5 1 6 8 7 2 4 8 3 0
8 9 2 8 5 8 0 7 4 0 4
3 2 7 9 1 8 4 4 8 2 8
7 4 7 5 6 7 1 0 1 9 5
5 2 6 8 7 3 5 6 8 3 5
7 8 3 8 2 6 1 6 8 6 3
8 5 2 1 8 5 4 9 2 2 7
1 8 0 9 9 6 0 3 2 4 7
7 0 6 5 1 7 4 9 2 1 3
2 2 6 8 0 7 5 1 4 5 9
9
4 7 7 4 8 9 4 4 9
9 1 6 0 4 6 4 9 0
2 3 9 1 5 0 7 6 6
3 1 8 8 8 1 2 1 1
6 6 1 0 7 2 5 3 7
7 0 1 8 5 7 2 8 7
4 9 2 1 8 4 7 0 6
6 9 8 1 5 2 4 9 7
3 7 2 3 6 8 1 8 8
8
9 2 5 3 1 0 2 5
8 3 1 7 7 3 4 6
2 7 9 4 0 6 2 7
5 5 8 8 3 2 1 8
7 8 7 3 0 4 6 5
7 5 3 6 5 5 4 1
8 3 1 8 5 6 7 8
0 3 6 9 0 4 1 5
7
6 6 3 0 9 2 8
4 8 4 9 6 9 3
9 3 8 6 4 1 2
3 3 8 1 4 7 6
9 8 2 7 0 1 2
4 6 4 9 6 6 6
5 0 1 1 1 3 7
6
1 7 9 8 2 3
4 8 9 3 6 2
2 3 2 2 8 7
8 1 6 4 4 9
0 4 1 5 4 3
3 3 9 4 1 8
8
8 0 1 7 4 5 5 1
7 2 9 9 8 7 4 3
3 8 0 8 6 3 6 9
7 1 2 0 2 1 6 0
9 2 7 1 9 7 0 5
4 9 8 4 5 8 9 7
7 4 5 8 5 4 4 1
3 1 8 7 7 0 8 9
11
1 4 5 1 7 5 5 1 1 7 9
6 1 1 5 7 0 1 3 7 8 7
6 2 0 9 5 3 9 9 8 4 9
9 6 2 1 7 5 6 2 7 4 9
2 4 4 9 8 7 4 3 0 7 2
9 0 4 9 7 7 0 7 0 2 7
9 3 0 5 9 2 4 3 2 8 0
9 1 0 4 3 0 5 1 6 0 9
9 0 9 0 4 3 7 9 3 6 3
2 0 5 9 9 3 2 9 2 2 3
6 8 0 9 8 0 0 2 7 9 2
12
8 2 2 6 5 0 8 8 4 5 6 8
9 2 7 2 5 4 2 4 8 0 2 9
7 8 6 9 9 6 8 1 4 0 7 6
9 3 7 3 5 9 5 6 5 4 0 7
1 4 4 9 4 0 2 1 1 4 7 4
6 5 3 5 6 8 4 9 3 9 8 9
6 8 7 7 2 1 1 0 0 8 1 7
2 8 1 9 2 1 4 4 7 3 6 6
7 2 5 8 3 6 9 8 4 1 7 8
4 3 7 8 5 3 4 8 9 8 7 9
9 7 6 6 3 2 8 9 3 8 4 4
8 9 5 3 2 0 3 2 5 4 6 9
12
4 4 8 9 5 4 7 5 8 6 8 3
3 1 9 0 9 2 6 8 3 0 7 6
2 6 9 9 8 2 6 5 5 8 1 5
5 3 2 8 4 8 6 0 6 2 1 5
9 6 1 8 6 5 5 5 0 0 0 2
9 4 9 4 1 3 1 3 5 1 8 3
2 0 8 8 5 0 1 2 6 2 0 9
3 4 1 8 2 3 5 4 5 6 0 3
6 0 5 5 1 8 7 4 4 2 5 5
8 4 9 3 6 5 7 7 7 3 5 4
5 6 8 1 5 6 6 6 3 2 0 0
6 9 8 7 2 9 8 6 9 1 5 6
12
6 2 7 9 1 2 0 9 2 1 4 0
2 0 9 1 5 8 0 0 8 7 4 8
4 4 5 2 1 8 1 1 6 3 1 6
4 4 5 9 2 7 2 0 7 4 3 1
6 1 4 2 5 8 1 3 4 3 7 1
4 1 7 5 2 3 7 2 0 9 4 7
0 7 2 7 3 3 1 8 0 5 1 5
4 1 1 1 9 3 2 1 6 5 3 2
6 7 8 3 2 4 7 9 4 4 2 2
7 5 8 6 5 9 9 5 0 0 3 4
4 1 5 7 0 6 0 5 0 9 8 3
0 0 9 1 6 1 1 8 6 8 4 4
12
5 6 6 2 4 5 7 6 1 6 5 3
6 6 2 2 4 5 6 8 5 8 9 3
2 2 6 8 9 6 7 6 4 5 3 2
1 3 5 4 8 3 1 3 1 3 5 9
8 8 0 4 1 2 1 8 7 4 7 9
1 5 7 0 2 1 3 9 1 2 0 2
5 3 2 1 0 9 3 6 0 0 0 7
1 6 5 3 6 2 5 3 7 1 3 9
4 2 0 3 9 2 5 6 1 1 4 6
6 9 1 1 2 5 2 1 8 2 9 6
7 7 3 4 3 3 2 7 3 3 9 0
9 5 0 5 0 7 5 1 4 7 0 9
12
1 7 1 4 3 8 2 5 1 8 3 9
1 7 2 6 3 8 4 2 0 3 3 7
0 2 5 5 7 1 4 1 7 7 4 8
1 4 1 4 0 5 9 7 0 3 9 6
9 1 3 1 5 8 2 2 0 5 1 6
4 9 0 5 9 3 0 9 1 0 0 3
4 3 8 7 2 6 4 0 2 2 0 0
9 0 8 3 6 3 7 9 6 1 8 3
3 0 2 5 2 5 5 8 3 6 1 8
6 9 1 4 0 3 1 9 0 8 2 6
1 1 2 1 0 8 0 9 1 5 0 4
1 9 5 6 7 8 8 0 3 8 4 6
12
2 3 6 4 7 0 4 5 3 7 1 9
5 0 7 5 8 3 5 9 1 6 2 6
7 7 0 9 9 8 0 3 2 6 7 4
9 0 5 9 4 4 0 1 0 1 5 8
8 7 3 7 5 6 4 8 7 9 2 0
5 5 6 9 8 9 2 2 7 9 5 8
6 3 5 3 8 5 5 2 1 9 5 4
0 7 6 0 2 9 2 4 7 3 4 0
9 3 5 0 4 1 2 2 3 8 9 9
4 4 4 8 1 8 6 7 4 0 1 4
5 9 4 6 4 7 6 9 7 4 7 5
5 5 9 2 5 2 5 1 4 4 0 2
12
9 7 8 8 4 5 7 1 8 4 7 3
7 7 7 2 5 7 4 6 4 2 2 8
4 7 7 6 5 4 5 6 6 1 6 2
4 2 0 7 8 9 6 3 9 4 6 3
5 8 9 8 1 8 9 6 8 4 8 9
1 2 7 7 4 5 6 2 5 1 5 8
1 4 1 5 5 9 5 5 1 5 5 5
8 7 1 8 6 3 3 0 9 6 9 5
9 1 9 1 5 6 5 7 9 0 6 2
6 7 8 4 3 7 4 4 1 8 1 0
4 5 4 0 5 1 7 4 9 4 6 8
7 1 4 8 2 7 0 0 3 3 0 6

#1 7
#2 10
#3 22
#4 11
#5 29
#6 24
#7 21
#8 8
#9 36
#10 23
#11 41
#12 30
#13 15
#14 30
#15 22
#16 14
#17 33
#18 20
#19 43
#20 28
#21 32
#22 38
#23 30
#24 47
#25 39
#26 12
#27 34
#28 22
#29 24
#30 22
#31 14
#32 16
#33 28
#34 36
#35 22
#36 21
#37 38
#38 31
#39 25
#40 24
#41 21
#42 29
#43 39
#44 41
#45 35
#46 37
#47 45
#48 45
#49 40
#50 35

#include <iostream>
using namespace std;
int arr[15][15];
int vis[15][15];
int n, ans;
int dx[2] = {0, 1};
int dy[2] = {1, 0};
void dfs(int x, int y, int cst)
{
if(x == n - 1 && y == n - 1)
{
if(cst < ans)
ans = cst;
}
vis[x][y]=1;
for(int k = 0; k < 2; k++)
{
int cx = x + dx[k];
int cy = y + dy[k];
int newcst;
if(cx >= 0 && cx < n && cy >= 0 && cy < n && vis[cx][cy] == 0)
{
if(arr[cx][cy] > arr[x][y])
newcst = cst + (arr[cx][cy] - arr[x][y]) + 1;
else
newcst = cst + 1;
dfs(cx, cy, newcst);
}
}
vis[x][y]=0;
}
int main()
{
freopen("input.txt", "r", stdin);
int test;
cin >> test;
for(int t = 1;t <= test; t++)
{
cin >> n;
for(int i = 0; i < n; i++)
{
for(int j = 0; j < n; j++)
{
vis[i][j] = 0;
cin >> arr[i][j];
}
}
ans = 9999;
dfs(0, 0, 0);
cout << "#" << t << " " << ans << endl;
}
return 0;
}

===========================================

#include<iostream>
using namespace std;

int arr[13][13], n, vis[13][13], minEne;
void reset() {
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
vis[i][j] = 0;
}
}
}
bool isSafe(int x, int y) {
if (x >= 0 && x < n && y >= 0 && y < n)
return true;
return false;
}
void dfs(int i, int j , int ene) {
if (ene > minEne) {
return;
}
if (i == n - 1 && j == n - 1) {
if (ene < minEne) {
minEne = ene;
return;
}
}
vis[i][j] = 1;
if (isSafe(i + 1, j) && vis[i + 1][j] == 0) {
if (arr[i + 1][j] <= arr[i][j])
dfs(i + 1, j, ene + 1);
else
dfs(i + 1, j, ene + arr[i + 1][j] - arr[i][j] + 1);
}
if (isSafe(i, j + 1) && vis[i][j + 1] == 0) {
if (arr[i][j+1] <= arr[i][j])
dfs(i, j+1, ene + 1);
else
dfs(i, j+1, ene + arr[i][j+1] - arr[i][j] + 1);
}
vis[i][j] = 0;
}
int main() {
freopen("input.txt", "r", stdin);
int t;
cin >> t;
for (int tc = 1; tc <= t; tc++) {
cin >> n;
for (int i = 0; i < n; i++) {
for (int j = 0; j < n; j++) {
cin >> arr[i][j];
}
}
reset();
vis[0][0] = 0;
minEne = 99999;
dfs(0, 0, 0);
cout <<"#"<<tc<<" "<< minEne<<endl;
}
return 0;
}```