# Graph II - Minimum Spanning Tree

Time Limit : 1 sec, Memory Limit : 131072 KB
Japanese version is here

# Minimum Spanning Tree

For a given weighted graph $G = (V, E)$, find the minimum spanning tree (MST) of $G$ and print total weight of edges belong to the MST.

## Input

In the first line, an integer $n$ denoting the number of vertices in $G$ is given. In the following $n$ lines, a $n \times n$ adjacency matrix $A$ which represents $G$ is given. $a_{ij}$ denotes the weight of edge connecting vertex $i$ and vertex $j$. If there is no edge between $i$ and $j$, $a_{ij}$ is given by -1.

## Output

Print the total weight of the minimum spanning tree of $G$.

## Constraints

• $1 \leq n \leq 100$
• $0 \leq a_{ij} \leq 2,000$ (if $a_{ij} \neq -1$)
• $a_{ij} = a_{ji}$
• $G$ is a connected graph

## Sample Input 1

5
-1 2 3 1 -1
2 -1 -1 4 -1
3 -1 -1 1 1
1 4 1 -1 3
-1 -1 1 3 -1


## Sample Output 1

5


## Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.