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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
//#include <boost/multiprecision/cpp_int.hpp> 
//using boost::multiprecision::cpp_int;
using namespace std;
#define ll long long int
#define F first
#define S second
//#define endl "\n"
//#define nl cout<<endl;
#define pb push_back
#define ull unsigned long long 
#define f(i,a,b) for(ll i=a;i<b;i++)
#define Knucklehead ios_base::sync_with_stdio(false);cin.tie(NULL);
//#define mod 100000007
#define mat vector<vector<ll>>
mat cn(ll n, ll m){return vector< vector<ll> >(n, vector<ll>(m));}
bool compare(char &s1,char &s2){return s1 > s2;} 
bool sortmahstyle(const pair<ll,ll> &a,  const pair<ll,ll> &b) 
{ 
    if(a.second > b.second )
        return true;
    if( a.second==b.second && a.first > b.second )
       return true;
    return false;
}
bool cmp(int n, pair<int, int> const& p)
{
    return (p.first < n);
}
//me
ll const mod = 1e9+7;//998244353;
ll const inf = 1e18;
ll const maxn = 2e5+1;


void solve()
{    

     ll h,w; cin >> h >> w;
     ll a[h][w];
     ll c[10][10];

     f(i,0,10)f(j,0,10) cin >> c[i][j];
     f(i,0,h)f(j,0,w) cin >> a[i][j];

     for(ll k=0; k<10; k++)
          for(ll i=0; i<10; i++){
               for(ll j=0; j<10; j++){
                    c[i][j] = min(c[i][j], c[i][k]+c[k][j]);
          }
     }

     ll tot = 0;
     f(i,0,h)f(j,0,w){
          if(a[i][j]!=-1)
               tot += c[a[i][j]][1];
     }
     cout << tot ;
     
}

int main() {
Knucklehead 
//*
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
/**/ 
          
          ll t;
          /**/t=1;
          /*/cin>>t;/**/
          f(testcases,0,t){
               //cout << "Case #" <<testcases+1<<": ";
               solve();
          }
 
 
    return 0;
}