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 Go (1.6) (judge verdict: Accepted)

package main

import (
	. "fmt"
	"bufio"
	"os"
	"strconv"
)

const INF int = 1e9
const LINF int64 = 1e9
const MOD int = INF + 7

func main() {
	next := newScanner()
	h, w := next.Int(), next.Int()
	c := make([][]int, 10)
	for i := 0; i < 10; i++ {
		for j := 0; j < 10; j++ {
			a := next.Int()

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

	ans := 0
	for i := 0; i < h; i++ {
		for j := 0; j < w; j++ {
			a := next.Int()

			if a == -1 {
				continue
			} else {
				ans += c[a][1]
			}
		}
	}

	Println(ans)
}

// Scanner begin

type scanner struct {
	r	*bufio.Reader
	buf []byte
	p	int
}

func newScanner() *scanner {
	return &scanner{r: bufio.NewReaderSize(os.Stdin, 10000)}
}

func (s *scanner) next() string {
	s.pre()
	start := s.p

	for ; s.p < len(s.buf); s.p++ {
		if s.buf[s.p] == ' ' {
			break
		}
	}

	result := string(s.buf[start:s.p])
	s.p++
	return result
}

func (s *scanner) Line() string {
	s.pre()
	start := s.p
	s.p = len(s.buf)

	return string(s.buf[start:])
}

func (s *scanner) Int() int {
	v, _ := strconv.Atoi(s.next())
	return v
}

func (s *scanner) Int64() int64 {
	v, _ := strconv.ParseInt(s.next(), 10, 64)
	return v
}

func (s *scanner) Float() float32 {
	f, _ := strconv.ParseFloat(s.next(), 32)

	return float32(f)
}

func (s *scanner) Float64() float64 {
	f, _ := strconv.ParseFloat(s.next(), 64)

	return f
}

func (s *scanner) Bool() bool {
	b, _ := strconv.ParseBool(s.next())

	return b
}

func (s *scanner) String() string {
	return s.next()
}


func (s *scanner) pre() {
	if s.p >= len(s.buf) {
		s.readLine()
		s.p = 0
	}
}

func (s *scanner) readLine() {
	s.buf = make([]byte, 0)
	for {
		l, p, e := s.r.ReadLine()
		if e != nil {
			panic(e)
		}
		s.buf = append(s.buf, l...)
		if !p {
			break
		}
	}
}

// Scanner end

// Standard Function begin

func Itob(i int) bool {
	if i == 0 {
		return false
	} else {
		return true
	}
}

func Btoi(f bool) int {
	if f {
		return 1
	} else {
		return 0
	}
}

func min(a ...int) int {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func max(a ...int) int {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minInt64(a ...int64) int64 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxInt64(a ...int64) int64 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minFloat(a ...float32) float32 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxFloat(a ...float32) float32 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func minFloat64(a ...float64) float64 {
	ret := a[0]
	for _, e := range a {
		if e < ret {
			ret = e
		}
	}

	return ret
}

func maxFloat64(a ...float64) float64 {
	ret := a[0]
	for _, e := range a {
		if e > ret {
			ret = e
		}
	}

	return ret
}

func abs(a int) int {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absInt64(a int64) int64 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absFloat(a float32) float32 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

func absFloat64(a float64) float64 {
	if a < 0 {
		return -a
	} else {
		return a
	}
}

// Standard Struct begin

type pair struct {
	first, second int
}

type pairs []pair

func Newpair() *pair {
	return &pair {
		first : 0,
		second : 0,
	}
}

func (p pairs) Less(i, j int) bool {
	if p[i].first < p[j].first {
		return true
	} else if p[i].first == p[j].first {
		return p[i].second < p[j].second
	} else {
		return false
	}
}