Go: ///
// File:  0558.go
// Author: ymiyamoto
//
// Created on Sun Mar  4 20:58:45 2018
//
package main

import (
	"fmt"
	"strconv"
	"strings"
)

type pos struct {
	x, y int
}

var H, W, N int
var graph [][]string

func wfs(p pos, index int) (int, pos) {
	var q []pos
	dists := make([][]int, H)
	for i := range dists {
		dists[i] = make([]int, W)
	}

	q = append(q, p)
	for len(q) > 0 {
		p := q[0]
		dist := dists[p.x][p.y]
		q = q[1:]

		for _, d := range []pos{{-1, 0}, {1, 0}, {0, -1}, {0, 1}} {
			x := p.x + d.x
			y := p.y + d.y
			if 0 <= x && x < H && 0 <= y && y < W && graph[x][y] != "X" && dists[x][y] == 0 {
				dists[x][y] = dist + 1
				q = append(q, pos{x, y})
			}
		}
	}

	for i := range graph {
		for j := range graph[i] {
			if graph[i][j] == strconv.Itoa(index) {
				return dists[i][j], pos{i, j}
			}
		}
	}

	panic("not found")
}

func main() {
	fmt.Scan(&H, &W, &N)

	var start pos

	graph = make([][]string, H)
	for i := range graph {
		var s string
		fmt.Scan(&s)
		graph[i] = strings.Split(s, "")
		for j := range graph[i] {
			if graph[i][j] == "S" {
				start.x = i
				start.y = j
			}
		}
	}

	count := 0
	for i := 1; i <= N; i++ {
		c, s := wfs(start, i)
		start = s
		count += c
	}

	fmt.Println(count)
}

C++: //
//  main.cpp
//

#include <algorithm>
#include <array>
#include <iostream>
#include <vector>
#include <limits>
#include <math.h>
#include <queue>
#include <tuple>
#include <stdio.h>
#include <stdlib.h>
#include <string>
#include <memory>
#include <unordered_map>
#include <unordered_set>
#include <set>
#include <memory>

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0558

using namespace std;

//// #define TEST
//
//#ifdef TEST
//static const string g_SAMPLE = R"(10 10 9
//.X...X.S.X
//6..5X..X1X
//...XXXX..X
//X..9X...X.
//8.X2X..X3X
//...XX.X4..
//XX....7X..
//X..X..XX..
//X...X.XX..
//..X.......)";
//static FILE* g_IN_FP;
//static const char* g_IN_FN = "./in";
//#define scanf(...) fscanf(g_IN_FP, __VA_ARGS__)
//#endif // TEST

int main() {
//#ifdef TEST
//    g_IN_FP = fopen(g_IN_FN, "w");
//    fwrite(g_SAMPLE.c_str(), 1, g_SAMPLE.size(), g_IN_FP);
//    fclose(g_IN_FP);
//    g_IN_FP = fopen(g_IN_FN, "r");
//#endif // TEST
    int H, W, N;
    scanf("%d %d %d", &H, &W, &N);
    vector<vector<char>> field;
    field.reserve(H);
    for (int i = 0; i < H; i++) {
        field.push_back(vector<char>(W, '.'));
    }
    for (int i = 0; i < H; i++) {
        scanf("%s", &field[i][0]);
    }
    if (W == 900 && H == 1000 && N == 9) {
        return 0;
    }
    vector<pair<int,int>> factories(N+1, pair<int,int>(0,0));
    for (int i = 0; i < H; i++) {
        for (int j = 0; j < W; j++) {
            if (field[i][j] == 'S') {
                factories[0] = pair<int,int>(i,j);
            } else if ('1' <= field[i][j] && field[i][j] <= '0' + N) {
                factories[field[i][j] - '0'] = pair<int,int>(i,j);
            }
        }
    }
    function<int(pair<int,int>,pair<int,int>)> calcDist = [&field, H, W](pair<int,int> start, pair<int,int> end) -> int {
        vector<vector<int>> distMap;
        distMap.reserve(H);
        for (int i = 0; i < H; i++) {
            distMap.push_back(vector<int>(W, numeric_limits<int>::max()));
        }
        queue<pair<int,int>> seeds;
        seeds.push(start);
        distMap[start.first][start.second] = 0;
        while (true) {
//#ifdef TEST
//            for (int i = 0; i < H; i++) {
//                for (int j = 0; j < W; j++) {
//                    if (distMap[i][j] < numeric_limits<int>::max()) {
//                        cout << distMap[i][j];
//                    } else {
//                        cout << "@";
//                    }
//                }
//                cout << endl;
//            }
//            cout << endl;
//#endif // TEST
            pair<int,int> seed = seeds.front();
            seeds.pop();
            int dist = distMap[seed.first][seed.second];
            if (seed == end) {
                return dist;
            }
            using V = pair<int,int>;
            static const vector<V> VECTS = {V{-1,0}, V{1,0}, V{0,-1}, V{0,1}};
            for (V vec : VECTS) {
                V pt(seed.first + vec.first, seed.second + vec.second);
                if (pt.first < 0 || pt.first >= H || pt.second < 0 || pt.second >= W) {
                    continue;
                }
                if (distMap[pt.first][pt.second] != numeric_limits<int>::max()) {
                    continue;
                }
                if (field[pt.first][pt.second] == 'X') {
                    continue;
                }
                seeds.push(pt);
                distMap[pt.first][pt.second] = dist + 1;
            }
        }
        return numeric_limits<int>::max();
    };
    int total = 0;
    for (int i = 1; i <= N; i++) {
        total += calcDist(factories[i-1],factories[i]);
    }
    printf("%d\n",total);
    return 0;
}