We have a weighted directed graph with N vertices numbered 0 to N-1.

The graph initially has N-1 edges. The $i-th edge (0 \leq i \leq N-2)$ is directed from Vertex i to Vertex i+1 and has a weight of 0.

Snuke will now add a new edge (i → j) for every pair $i, j (0 \leq i,j \leq N-1$,\ $i \neq j)$. The weight of the edge will be -1 if i < j, and 1 otherwise.

Ringo is a boy. A negative cycle (a cycle whose total weight is negative) in a graph makes him sad. He will delete some of the edges added by Snuke so that the graph will no longer contain a negative cycle. The cost of deleting the edge (i → j) is A_{i,j}. He cannot delete edges that have been present from the beginning.

Find the minimum total cost required to achieve Ringo's objective.

Constraints

• $3 \leq N \leq 500$
• $1 \leq A_{i,j} \leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
$A_{0,1} A_{0,2} A_{0,3} \cdots A_{0,N-1}$
$A_{1,0} A_{1,2} A_{1,3} \cdots A_{1,N-1}$
$A_{2,0} A_{2,1} A_{2,3} \cdots A_{2,N-1}$
$\vdots$
$A_{N-1,0} A_{N-1,1} A_{N-1,2} \cdots A_{N-1,N-2}$

Output

Print the minimum total cost required to achieve Ringo's objective.

Examples

Input

3
2 1
1 4
3 3

Output

2

Input

4
1 1 1
1 1 1
1 1 1
1 1 1

Output

2

Input

10
190587 2038070 142162180 88207341 215145790 38 2 5 20
32047998 21426 4177178 52 734621629 2596 102224223 5 1864
41 481241221 1518272 51 772 146 8805349 3243297 449
918151 126080576 5186563 46354 6646 491776 5750138 2897 161
3656 7551068 2919714 43035419 495 3408 26 3317 2698
455357 3 12 1857 5459 7870 4123856 2402 258
3 25700 16191 102120 971821039 52375 40449 20548149 16186673
2 16 130300357 18 6574485 29175 179 1693 2681
99 833 131 2 414045824 57357 56 302669472 95
8408 7 1266941 60620177 129747 41382505 38966 187 5151064

Output

2280211

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