Problem Statement

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.