Problem Statement

On a two-dimensional plane, you are now at coordinate ~(1, 1)~ and want to get to ~(R, C)~ , the coordinates of the UFO.
When you are at ~(r, c)~ , you can make the following four kinds of moves:

• Move from ~(r, c)~ to ~(r, c + 1)~ at the cost of ~A_{r, c}~ . You can make this move when ~c < C~ .
• Move from ~(r, c)~ to ~(r, c - 1)~ at the cost of ~A_{r, c - 1}~ . You can make this move when ~c > 1~ .
• Move from ~(r, c)~ to ~(r + 1, c)~ at the cost of ~B_{r, c}~ . You can make this move when ~r < R~ .
• Choose an integer ~i~ such that ~1 ≤ i < r~ and move from ~(r, c)~ to ~(r - i, c)~ at the cost of ~1 + i~ .

Find the minimum cost needed to move from ~(1, 1)~ to ~(R, C)~ .

Constraints

• All values in input are integers.
• ~2 ≤ R, C ≤ 500~
• ~0 ≤ A_{i,j} < 10^3~
• ~0 ≤ B_{i,j} < 10^3~

Input

Input is given from Standard Input in the following format:

~R~ ~C~

~A_{1,1}~ ~\cdots~ ~A_{1,C-1}~

~\vdots~

~A_{R,1}~ ~\cdots~ ~A_{R,C-1}~

~B_{1,1}~ ~\cdots~ ~B_{1,C}~

~\vdots~

~B_{R-1,1}~ ~\cdots~ ~B_{R-1,C}~

Output

Print the answer.

Sample Input 1

3 3
10 1
10 10
1 10
1 10 1
1 10 1

Sample Output 1

9

You can achieve the cost of ~9~ as follows:

• Move from ~(1, 1)~ to ~(2, 1)~ at the cost of ~1~ .
• Move from ~(2, 1)~ to ~(3, 1)~ at the cost of ~1~ .
• Move from ~(3, 1)~ to ~(3, 2)~ at the cost of ~1~ .
• Move from ~(3, 2)~ to ~(1, 2)~ at the cost of ~3~ .
• Move from ~(1, 2)~ to ~(1, 3)~ at the cost of ~1~ .
• Move from ~(1, 3)~ to ~(2, 3)~ at the cost of ~1~ .
• Move from ~(2, 3)~ to ~(3, 3)~ at the cost of ~1~ .

Sample Input 2

7 11
42 77 94 76 40 66 43 28 66 23
27 34 41 31 83 13 64 69 81 82
23 81 0 22 39 51 4 37 84 43
62 37 82 86 26 67 45 78 85 2
79 18 72 62 68 84 69 88 19 48
0 27 21 51 71 13 87 45 39 11
74 57 32 0 97 41 87 96 17 98
69 58 76 32 51 16 38 68 86 82 64
53 47 33 7 51 75 43 14 96 86 70
80 58 12 76 94 50 59 2 1 54 25
14 14 62 28 12 43 15 70 65 44 41
56 50 50 54 53 34 16 3 2 59 88
27 85 50 79 48 86 27 81 78 78 64

Sample Output 2

498

Sample Input 3

4 4
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0 0
0 0 0 0
0 0 0 0

Sample Output 3

0