Problem:
Score : 400 points

Problem Statement

Joisino the magical girl has decided to turn every single digit that exists on this world into 1.

Rewriting a digit i with j (0≤i,j≤9) costs c_{i,j} MP (Magic Points).

She is now standing before a wall. The wall is divided into HW squares in H rows and W columns, and at least one square contains a digit between 0 and 9 (inclusive).

You are given A_{i,j} that describes the square at the i-th row from the top and j-th column from the left, as follows:

If A_{i,j}≠-1, the square contains a digit A_{i,j}.

If A_{i,j}=-1, the square does not contain a digit.

Find the minimum total amount of MP required to turn every digit on this wall into 1 in the end.

Constraints

1≤H,W≤200

1≤c_{i,j}≤10^3 (i≠j)

c_{i,j}=0 (i=j)

-1≤A_{i,j}≤9

All input values are integers.

There is at least one digit on the wall.

Input

Input is given from Standard Input in the following format:

H W
c_{0,0} ... c_{0,9}
:
c_{9,0} ... c_{9,9}
A_{1,1} ... A_{1,W}
:
A_{H,1} ... A_{H,W}

Output

Print the minimum total amount of MP required to turn every digit on the wall into 1 in the end.

Sample Input 1

2 4
0 9 9 9 9 9 9 9 9 9
9 0 9 9 9 9 9 9 9 9
9 9 0 9 9 9 9 9 9 9
9 9 9 0 9 9 9 9 9 9
9 9 9 9 0 9 9 9 9 2
9 9 9 9 9 0 9 9 9 9
9 9 9 9 9 9 0 9 9 9
9 9 9 9 9 9 9 0 9 9
9 9 9 9 2 9 9 9 0 9
9 2 9 9 9 9 9 9 9 0
-1 -1 -1 -1
8 1 1 8

Sample Output 1

12

To turn a single 8 into 1, it is optimal to first turn 8 into 4, then turn 4 into 9, and finally turn 9 into 1, costing 6 MP.

The wall contains two 8s, so the minimum total MP required is 6×2=12.

Sample Input 2

5 5
0 999 999 999 999 999 999 999 999 999
999 0 999 999 999 999 999 999 999 999
999 999 0 999 999 999 999 999 999 999
999 999 999 0 999 999 999 999 999 999
999 999 999 999 0 999 999 999 999 999
999 999 999 999 999 0 999 999 999 999
999 999 999 999 999 999 0 999 999 999
999 999 999 999 999 999 999 0 999 999
999 999 999 999 999 999 999 999 0 999
999 999 999 999 999 999 999 999 999 0
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1
1 1 1 1 1

Sample Output 2

0

Note that she may not need to change any digit.

Sample Input 3

3 5
0 4 3 6 2 7 2 5 3 3
4 0 5 3 7 5 3 7 2 7
5 7 0 7 2 9 3 2 9 1
3 6 2 0 2 4 6 4 2 3
3 5 7 4 0 6 9 7 6 7
9 8 5 2 2 0 4 7 6 5
5 4 6 3 2 3 0 5 4 3
3 6 2 3 4 2 4 0 8 9
4 6 5 4 3 5 3 2 0 8
2 1 3 4 5 7 8 6 4 0
3 5 2 6 1
2 5 3 2 1
6 9 2 5 6

Sample Output 3

47

Solution in Rust (1.42.0) (judge verdict: Accepted)

#![allow(clippy::needless_range_loop)]
#![allow(unused_macros)]
#![allow(dead_code)]

use proconio::input;
use proconio::marker::*;

use std::cmp::*;
use std::collections::binary_heap::BinaryHeap;
#[derive(Copy, Clone, Eq, PartialEq)]
struct GraphEdge {
    node_to: usize,
    cost: isize,
}
impl Ord for GraphEdge {
    fn cmp(&self, other: &GraphEdge) -> Ordering {
        other.cost.cmp(&self.cost)
    }
}
impl PartialOrd for GraphEdge {
    fn partial_cmp(&self, other: &GraphEdge) -> Option<Ordering> {
        Some(self.cmp(other))
    }
}
impl GraphEdge {
    fn new(node_to: usize, cost: isize) -> Self {
        Self { node_to, cost }
    }
}
struct Graph {
    pub edges: Vec<Vec<GraphEdge>>,
    pub nodes: usize,
}
impl Graph {
    fn new(nodes: usize) -> Self {
        Self {
            edges: vec![vec![]; nodes],
            nodes,
        }
    }
    fn edge_undirected(&mut self, node_a: usize, node_b: usize) {
        self.edges[node_a].push(GraphEdge::new(node_b, 1));
        self.edges[node_b].push(GraphEdge::new(node_a, 1));
    }
    fn edge_directed(&mut self, node_from: usize, node_to: usize) {
        self.edges[node_from].push(GraphEdge::new(node_to, 1));
    }
    fn edge_undirected_costed(&mut self, node_a: usize, node_b: usize, cost: isize) {
        self.edges[node_a].push(GraphEdge::new(node_b, cost));
        self.edges[node_b].push(GraphEdge::new(node_a, cost));
    }
    fn edge_directed_costed(&mut self, node_from: usize, node_to: usize, cost: isize) {
        self.edges[node_from].push(GraphEdge::new(node_to, cost));
    }
    fn dijkstra(&self, node_from: usize) -> Vec<isize> {
        let mut costs = vec![std::isize::MAX; self.nodes];
        let mut heap: BinaryHeap<GraphEdge> = BinaryHeap::new();
        heap.push(GraphEdge::new(node_from, 0));
        while let Some(GraphEdge { cost, node_to }) = heap.pop() {
            if cost >= costs[node_to] {
                continue;
            }
            costs[node_to] = cost;
            for edge in &self.edges[node_to] {
                let next = GraphEdge::new(edge.node_to, cost + edge.cost);
                heap.push(next);
            }
        }
        costs
    }
    fn warshall_floyd(&self) -> Vec<Vec<isize>> {
        let mut costs = vec![vec![std::isize::MAX; self.nodes]; self.nodes];
        for i in 0..self.nodes {
            costs[i][i] = 0;
        }
        for (node_from, edges) in self.edges.iter().enumerate() {
            for GraphEdge { node_to, cost } in edges.iter() {
                costs[node_from][*node_to] = *cost;
            }
        }
        for k in 0..self.nodes {
            for i in 0..self.nodes {
                for j in 0..self.nodes {
                    costs[i][j] =
                        std::cmp::min(costs[i][j], costs[i][k].saturating_add(costs[k][j]));
                }
            }
        }
        costs
    }
}

fn main() {
    input! {
        h: usize,
        w: usize,
        c: [[isize; 10]; 10],
        a: [isize; h * w],
    }
    let mut graph = Graph::new(10);
    for (node_from, costs) in c.iter().enumerate() {
        for (node_to, cost) in costs.iter().enumerate() {
            graph.edge_directed_costed(node_from, node_to, *cost);
        }
    }
    let costs = graph.warshall_floyd();
    let ans: isize = a
        .iter()
        .filter(|x| **x != -1)
        .map(|x| costs[*x as usize][1])
        .sum();
    println!("{}", ans);
}