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)

#pragma region template
// clang-format off
#ifdef ONLINE_JUDGE
  #define here
  #define com(msg)
  #define watch(...)
  #define watchVec(vec)
  #define local(x)
  #define alter(x,y) y
#else
  #define here cerr<<__func__<<"/"<<__LINE__<<": reached\n"
  #define com(msg) cerr<<"{ "<<msg<< " }\n"
  #define watch(...) observe(#__VA_ARGS__,__VA_ARGS__)
  #define watchVec(vec) do{cerr<<#vec<<": ";printv(#vec,vec);}while(0)
  #define local(x) do{x}while(0)
  #define alter(x,y) x
#endif

#include <bits/stdc++.h>
#include <boost/multiprecision/cpp_int.hpp>

#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define rep(i,n) for(int i=0;i<(n);i++)
#define brep(i,a,b) for(int i=(a);i<=(b);i++)
#define rrep(i,n) for(int i=(n)-1,now=0;i>=0;i--,now++)
#define rbrep(i,a,b) for(int i=(a),now=0;i>=(b);i--,now++)
#define xrep(i,n) for(int i=1;i<=(n);i++)
#define yes(n) cout<<((n)?YES:NO)<<"\n"
#define cco(...) prints(__VA_ARGS__)
#define Sort(v) sort((v).begin(),(v).end())
#define rSort(v) sort((v).rbegin(),(v).rend())
#define Rev(v) reverse((v).begin(),(v).end())
#define Unique(v) (v).erase(unique((v).begin(),(v).end()),(v).end())
#define inarea(p,a,b) (0<=(p.first)&&0<=(p.second)&&(p.first)<(a)&&(p.second)<(b))
#define in_area(y,x,a,b) (0<=(y)&&0<=(x)&&(y)<(a)&&(x)<(b))
#define in_range(x,a,b) ((a)<=(x)&&(x)<(b))

using namespace std;
using ll    = long long;
using ld    = long double;
using pt    = pair<int, int>;
using ull   = unsigned long long;
using str   = string;
using vbl   = vector<bool>;
using dqbl  = deque<bool>;
using vint  = vector<int>;
using vll   = vector<long long>;
using vdb   = vector<double>;
using vld   = vector<long double>;
using vpt   = vector<pair<int, int>>;
using vstr  = vector<string>;
using vvdb  = vector<vector<double>>;
using vvbl  = vector<vector<bool>>;
using vdqbl = vector<deque<bool>>;
using vvint = vector<vector<int>>;
using vvll  = vector<vector<long long>>;
using Int   = boost::multiprecision::cpp_int;

constexpr int       INF   = 1e9;
constexpr long long LINF  = 1e18;
constexpr double    EPS   = 1e-9;
constexpr int       dy[]  = {1,0,-1,0,1,1,-1,-1};
constexpr int       dx[]  = {0,1,0,-1,-1,1,1,-1};
constexpr pt        dv[]  = { {1,0},{0,1},{-1,0},{0,-1},{1,-1},{1,1},{-1,1},{-1,-1} };

// --- functions which take 1 argument --- //
template<class T> int sgn(const T &x){return (x>0)-(x<0);}
template<class S,class T=int> int digit(S x,const T &b=10){int r=1;while((x/=b)>=1)r++;return r;}
template<class T> double degToRad(const T &a){return a/180.0*M_PI;}
template<class T> double radToDeg(const T &a){return a/M_PI*180.0;}
template<class T> long long factorial(const T &n) {if(n==0)return 1;long long r=1;for(int i=2;i<=n;i++)r*=i;return r;}
template<class T> bool isPrime(const T &n){if(n<=1)return false;T i=2;while(i*i<=n){if(n%i==0&&n!=i)return false;i++;}return true;}
template<class T> map<T,T> factorize(T n){map<T,T>r;for(T i=2;i*i<=n;i++){while(n%i==0){r[i]++;n/=i;}}if(n!=1)r[n]=1;return r;}
template<class T> vector<T> divisor(const T &n){vector<T>r;for(T i=1;i*i<=n;i++){if(!(n%i)){r.emplace_back(i);if(i*i!=n)r.emplace_back(n/i);}}return r;}

// --- functions which take more than 1 argument --- //
template<class S,class T> [[maybe_unused]] bool chmax(S &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class S,class T> [[maybe_unused]] bool chmin(S &a,const T &b){if(a>b){a=b;return true;}return false;}
template<class S,class T> bool near(const S &a, const T &b){return abs(a-b)<EPS;}
template<class S,class T> long long bpow(S m,T n){long long r=1;while(n>0){if(n&1)r*=m;m*=m;n/=2;}return r;}
template<class S,class T> typename common_type<S,T>::type min(const S &m,const T &n){return min((typename common_type<S,T>::type)m,(typename common_type<S,T>::type)n);}
template<class S,class T> typename common_type<S,T>::type max(const S &m,const T &n){return max((typename common_type<S,T>::type)m,(typename common_type<S,T>::type)n);}
template<class S,class T> long long nPr(const S &n,const T &k){if(n<k||n<0||k<0)return 0;long long r=1;for(int i=n-k+1;i<=n;i++)r*=i;return r;}
template<class S,class T> long long nCr(const S &n,T k){if(n<k||n<0||k<0)return 0;long long r=1;k=min(k,n-k);for(int i=n-k+1;i<=n;i++)r*=i;return r/factorial(k);}
template<class T>            void prints(const T &v){cout<<v<<"\n";}
template<class S,class... T> void prints(const S &v,const T&... w){cout<<v<<" ";prints(w...);}

// --- functions which take vector/deque as argument --- //
template<class T> void printd(const vector<T> &v,const string &d){for(int i=0;i<(int)v.size()-1;i++)cout<<v[i]<<d;cout<<*v.rbegin()<<"\n";}
template<class T> void printd(const vector<vector<T>> &v,const string &d){for(const auto &x:v)printD(x,d);}
template<class T> bool in(const T &k,const vector<T> &v)          {return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const int &k,const vector<long long> &v){return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const long long &k,const vector<int> &v){return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const char &k,const string &v)          {return find(v.begin(),v.end(),k)!=v.end();}
                  bool in(const char* k,const vector<string> &v)  {return find(v.begin(),v.end(),k)!=v.end();}
template<class T> double veclen(const vector<T> &v){return sqrt(reduce(v.begin(),v.end(),0.0,[](T s,T k){return s+=k*k;}));}
template<class T> T min(const vector<T> &v){return *min_element(v.begin(),v.end());}
template<class T> T max(const vector<T> &v){return *max_element(v.begin(),v.end());}
template<class T> T sum(const vector<T> &v){return reduce(v.begin(),v.end(),(T)0);}
template<class T> T gcd(const vector<T> &v){T r=v[0];for(int i=1;i<v.size();i++)r=gcd(r,v[i]);return r;}
template<class T> T lcm(const vector<T> &v){T r=v[0];for(int i=1;i<v.size();i++)r=lcm(r,v[i]);return r;}
template<class T> T vectorAdd(const T &u,const T &v)     {T r(u.size());for(int i=0;i<u.size();i++)r[i]=u[i]+v[i];return r;}
template<class T> T vectorSubtract(const T &u,const T &v){T r(u.size());for(int i=0;i<u.size();i++)r[i]=u[i]-v[i];return r;}
template<class T> T vectorMultiply(const T &u,const T &v){T r(u.size());for(int i=0;i<u.size();i++)r[i]=u[i]*v[i];return r;}
template<class T> T vectorDivide(const T &u,const T &v)  {T r(u.size());for(int i=0;i<u.size();i++)r[i]=u[i]/v[i];return r;}
template<class T> T dotProduct(const deque<bool> &u,const vector<T> &v){T r=0;for(int i=0;i<u.size();i++)if(u[i])r+=v[i];return r;}
template<class S,class T> typename common_type<S,T>::type dotProduct(const vector<S> &u,const vector<T> &v){typename common_type<S,T>::type r=0;for(int i=0;i<u.size();i++)r+=u[i]*v[i];return r;}
template<class S,class T> void sortBySecond(vector<pair<S,T>> &v){sort(v.begin(),v.end(),[](auto &L,auto &R){if(L.second==R.second)return L.first<R.first;return L.second<R.second;});}

// --- functions which take set/map as argument --- //
template<class T> T min(const set<T> &v){return *min_element(v.begin(),v.end());}
template<class T> T max(const set<T> &v){return *max_element(v.begin(),v.end());}
template<class T> T sum(const set<T> &v){return reduce(v.begin(),v.end(),(T)0);}
template<class T> T gcd(const set<T> &v){T r=0;for(const T &x:v)r=(r==0)?x:gcd(r,x);return r;}
template<class T> T lcm(const set<T> &v){T r=0;for(const T &x:v)r=(r==0)?x:lcm(r,x);return r;}
template<class T> bool in(const T &k,const set<T> &v){return find(v.begin(),v.end(),k)!=v.end();}
template<class S,class T> pair<S,T> min(const map<S,T> &m){pair<S,T> r=*m.begin();for(const pair<S,T> &p:m)if(r.second>p.second)r=p;return r;}
template<class S,class T> pair<S,T> max(const map<S,T> &m){pair<S,T> r=*m.begin();for(const pair<S,T> &p:m)if(r.second<p.second)r=p;return r;}

// --- operators --- //
template<class T>         istream& operator>>(istream &i,vector<T> &v){cin.tie(nullptr);ios::sync_with_stdio(false);for(T &x:v)i>>x;return i;}
template<class T>         ostream& operator<<(ostream &o,vector<T> &v){for(T &x:v)o<<x<<"\n";return o;}
template<class S,class T> istream& operator>>(istream &i,pair<S,T> &p){i>>p.first>>p.second;return i;}
template<class S,class T> ostream& operator<<(ostream &o,pair<S,T> &p){o<<p.first<<" "<<p.second<<"\n";return o;}
template<class S,class T> pair<S,T> operator+(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first+q.first,p.second+q.second};}
template<class S,class T> pair<S,T> operator-(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first-q.first,p.second-q.second};}
template<class S,class T> pair<S,T> operator*(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first*q.first,p.second*q.second};}
template<class S,class T> pair<S,T> operator/(const pair<S,T> &p,const pair<S,T> &q){return pair<S,T>{p.first/q.first,p.second/q.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator--(pair<S,T> &p){return pair<S,T>{--p.first,--p.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator++(pair<S,T> &p){return pair<S,T>{++p.first,++p.second};}
template<class S,class T> [[maybe_unused]] pair<S,T> operator+=(pair<S,T> &p,const pair<S,T> &q){return p=p+q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator-=(pair<S,T> &p,const pair<S,T> &q){return p=p-q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator*=(pair<S,T> &p,const pair<S,T> &q){return p=p*q;}
template<class S,class T> [[maybe_unused]] pair<S,T> operator/=(pair<S,T> &p,const pair<S,T> &q){return p=p/q;}

// --- functions for debugging --- //
template<class T>            void observe(const char *n,T &&v)         {cerr<<n<<": "<<v<<"\n";}
template<class S,class... T> void observe(const char *n,S &&v,T&&... w){const char *c=strchr(n+1,',');cerr.write(n,c-n)<<": "<<v<<" |";observe(c+1,w...);}
template<class T> void printv([[maybe_unused]] const char *n, const vector<T> &v){cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class T> void printv([[maybe_unused]] const char *n, const deque<T> &v) {cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class T> void printv([[maybe_unused]] const char *n, const set<T> &v)   {cerr<<"[ ";for(const T &x:v)cerr<<x<<" ";cerr<<"]\n";}
template<class P> void printv([[maybe_unused]] const char *n, const P &p){cerr<<"{ "<<p.first<<" "<<p.second<<" } ";}
template<class T> void printv(const char *n, const vector<vector<T>> &v){bool f=0;for(const vector<T> &x:v){if(f)cerr<<string(strlen(n)+2,' ');f=1;printv<T>("",x);}}
template<class T> void printv(const char *n, const vector<deque<T>> &v) {bool f=0;for(const deque<T> &x:v){if(f)cerr<<string(strlen(n)+2,' ');f=1;printv<T>("",x);}}
template<class S,class T> void printv([[maybe_unused]] const char *n, const map<S,T> &m) {cerr<<"[ ";for(const pair<S,T> &p:m)cerr<<"{ "<<p.first<<", "<<p.second<<" } ";cerr<<"]\n";}
template<class S,class T> void printv([[maybe_unused]] const char *n, const vector<pair<S,T>> &v){cerr<<"[ ";for(const pair<S,T> &p:v)printv<pair<S,T>>("",p);cerr<<"]\n";}
template<class S,class T> void printv([[maybe_unused]] const char *n, const deque<pair<S,T>> &v){cerr<<"[ ";for(const pair<S,T> &p:v)printv<pair<S,T>>("",p);cerr<<"]\n";}
// clang-format on
#pragma endregion

void solve(int H, int W, vector<vector<int>> c, vector<vector<int>> A) {
  rep(k, 10) {
    rep(i, 10) {
      rep(j, 10) {
        chmin(c[i][j], c[i][k] + c[k][j]);
      }
    }
  }

  int ans = 0;

  rep(i, H) {
    rep(j, W) {
      if (A[i][j] != -1) ans += c[A[i][j]][1];
    }
  }

  cout << ans << "\n";
}

// clang-format off
int main() {
  #pragma GCC diagnostic push
  #pragma GCC diagnostic ignored "-Wunused-result"
  int H;
  scanf("%d",&H);
  int W;
  scanf("%d",&W);
  vector<vector<int>> c(9-0+1, vector<int>(9-0+1));
  for(int i = 0 ; i < 9-0+1 ; i++){
    for(int j = 0 ; j < 9-0+1 ; j++){
      scanf("%d",&c[i][j]);
    }
  }
  vector<vector<int>> A(H, vector<int>(W));
  for(int i = 0 ; i < H ; i++){
    for(int j = 0 ; j < W ; j++){
      scanf("%d",&A[i][j]);
    }
  }
  #pragma GCC diagnostic pop
  solve(H, W, move(c), move(A));
  exit(EXIT_SUCCESS);
}