Go: // BFS

package main

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

var scanner = bufio.NewScanner(os.Stdin)

var p = [15]int{}
var g = [13][4]int {
	// -1は存在しないマス目
	{2,-1,-1,-1},
	{2,5,-1,-1},{0,1,3,6},{2,7,-1,-1},
	{5,-1,-1,-1},{1,4,6,9},{2,5,7,10},{3,6,8,11},{7,-1,-1,-1},
	{5,10,-1,-1},{6,9,11,12},{7,10,-1,-1},
	{10,-1,-1,-1},
}

/*
　  ０ １ ２ ３ ４
 0 |／|／|  |／|／|
 1 |／|　|  |　|／|
 2 |　|　|  |　|　|
 3 |／|　|  |　|／|
 4 |／|／|  |／|／|
*/

var row = [13]int{0,1,1,1,2,2,2,2,2,3,3,3,4}
var col = [13]int{2,1,2,3,0,1,2,3,4,1,2,3,2}

type wolf struct {
	m [13]int
}

type pair struct {
	first wolf
	second int
}

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

func print_board(board [13]int) {
	fmt.Println("--------------------------")
	fmt.Printf("        [%2d]\n", board[0])
	fmt.Printf("    [%2d][%2d][%2d]\n", board[1], board[2], board[3])
	fmt.Printf("[%2d][%2d][%2d][%2d][%2d]\n", board[4], board[5], board[6], board[7], board[8])
	fmt.Printf("    [%2d][%2d][%2d]\n", board[9], board[10], board[11])
	fmt.Printf("        [%2d]\n", board[12])
	fmt.Println("--------------------------")
}

func main() {
	for scanner.Scan() {
		p1, _ := strconv.Atoi(scanner.Text())
		if p1 == -1 {
			break
		}
		p[0]= p1
		scanner.Scan()
		buf1 := strings.Split(scanner.Text(), " ")
		p2, _ := strconv.Atoi(buf1[0])
		p3, _ := strconv.Atoi(buf1[1])
		p4, _ := strconv.Atoi(buf1[2])
		p[1], p[2], p[3] = p2, p3, p4
		scanner.Scan()
		buf2 := strings.Split(scanner.Text(), " ")
		p5, _ := strconv.Atoi(buf2[0])
		p6, _ := strconv.Atoi(buf2[1])
		p7, _ := strconv.Atoi(buf2[2])
		p8, _ := strconv.Atoi(buf2[3])
		p9, _ := strconv.Atoi(buf2[4])
		p[4], p[5], p[6], p[7], p[8] = p5, p6, p7, p8, p9
		scanner.Scan()
		buf3 := strings.Split(scanner.Text(), " ")
		p10, _ := strconv.Atoi(buf3[0])
		p11, _ := strconv.Atoi(buf3[1])
		p12, _ := strconv.Atoi(buf3[2])
		p[9], p[10], p[11] = p10, p11, p12
		scanner.Scan()
		p13, _ := strconv.Atoi(scanner.Text())
		p[12] = p13
		S := make(map[wolf]struct{})
		st := wolf{}
		for i := 0; i < 13; i++ {
			st.m[i] = p[i]
		}
		Q := make([]pair, 0)
		S[st] = struct{}{}
		Q = append(Q, pair{st, 0})
		yet := true
		for len(Q) > 0 {
			at := Q[0].first
			print_board(at.m)
			cost := Q[0].second
			Q = Q[1:]
			ok := true
			for i :=1; i < 12; i++ {
				if at.m[i] != i {
					ok = false
				}
			}
			if ok {
				print_board(at.m)
				yet = false
				fmt.Println(cost)
				break
			}
			now := cost
			for i := 0; i < 13; i++ {
				if at.m[i] != 0 {
					now += abs(row[i]-row[at.m[i]]) + abs(col[i]-col[at.m[i]])
				}
			}
			if now > 20 {
				continue
			}
			for i := 0; i < 13; i++ {
				if at.m[i] == 0 {
					for j := 0; j < 4; j++ {
						if ^g[i][j] != 0 {
							at.m[i], at.m[g[i][j]] = at.m[g[i][j]], at.m[i]
							if _, ok := S[at]; !ok {
								S[at] = struct{}{}
								Q = append(Q, pair{at, cost+1})
							}
							at.m[i], at.m[g[i][j]] = at.m[g[i][j]], at.m[i]
						}
					}
				}
			}
		}
		if yet {
			fmt.Println("NA")
		}
	}
}

C++: #include <cmath>
#include <iostream>
#include <string>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <array>
#include <sstream>
using namespace std;
#ifdef _MSC_VER
#include "_lib_msc.h"
#endif
#define ITER(c)             __typeof__((c).begin())
#define REP(i, n)           for(int(i)=0;(i)<(n);++(i))
template<class _T> _T MAX(_T p1,_T p2){return (p2<p1)?p1:p2;} 
template<class _T> _T MIN(_T p1,_T p2){return (p1<p2)?p1:p2;} 
typedef vector<int> VI;
typedef vector<VI> VVI;
#define mp                  make_pair
#define pb                  push_back

const int inf = 1<<29;

typedef array<char,13> obj;
obj final  = {{0,1,2,3,4,5,6,7,8,9,10,11,0}};
obj final1 = {{2,1,0,3,4,5,6,7,8,9,0,11,10}};
obj final2 = {{2,1,0,3,4,5,6,7,8,9,10,11,0}};
obj final3 = {{0,1,2,3,4,5,6,7,8,9,0,11,10}};
int mov[][5] = {
    {2,-1},         // 0
    {2,5,-1},       // 1
    {0,1,3,6,-1},   // 2
    {2,7,-1},       // 3
    {5,-1},         // 4
    {1,4,6,9,-1},   // 5
    {2,5,7,10,-1},  // 6
    {3,6,8,11,-1},  // 7
    {7,-1},         // 8
    {5,10,-1},      // 9
    {6,9,11,12,-1}, // 10
    {7,10,-1},      // 11
    {10,-1},        // 12
};
int dtblm[5][5] = {
    {-1, -1,  0, -1, -1},
    {-1,  1,  2,  3, -1},
    { 4,  5,  6,  7,  8},
    {-1,  9, 10, 11, -1},
    {-1, -1, 12, -1, -1},
};
int dtbl[13][13];

void mktbl(){
    REP(y1,5) REP(x1,5){
        if(dtblm[y1][x1] == -1) continue;
        int k1 = dtblm[y1][x1];
        REP(y2,5) REP(x2,5){
            if(dtblm[y2][x2] == -1) continue;
            int k2 = dtblm[y2][x2];
            dtbl[k1][k2] = abs(x1-x2) + abs(y1-y2);
        }
    }
}

struct QOBJ{
    obj p;
    int sp[2];
    QOBJ(obj p, int sp1, int sp2) : p(p){sp[0]=sp1,sp[1]=sp2;}
};

int distance(const obj &p){
    int total = 0;
    REP(i,13){
        if(p[i] == 0) continue;
        total += dtbl[i][(int)(p[i])];
    }
    return total;
}

string solve(const obj &o){
    if(o == final) return "0";

    map<obj, int> memo;
    queue<QOBJ> q;
    int sp1 = -1, sp2 = -1;
    REP(i,13) if(o[i] == 0){
        if(sp1 == -1) sp1 = i; else sp2 = i;
    }
    q.push(QOBJ(o,sp1,sp2));
    memo[o] = 0;
    int maxstep = 20;

    while(!q.empty()){
        QOBJ &p = q.front();
        obj &pp = p.p;
        int step = memo[pp];
        if(step + distance(pp) < maxstep){
            REP(sp,2){
                int sps = p.sp[sp];
                REP(mi, 4){
                    int spd = mov[sps][mi];
                    if(spd == -1) break;
                    swap(pp[sps],pp[spd]);
                    ITER(memo) it = memo.find(pp);
                    if(it == memo.end() || it->second > step+1){
                        if(it == memo.end()){
                            memo[pp] = step+1;
                        } else {
                            it->second = step+1;
                        }
                        if(pp == final){
                            maxstep = step;
                        }
                            if(sp == 0){
                                q.push(QOBJ(pp,spd,p.sp[1]));
                            } else {
                                q.push(QOBJ(pp,p.sp[0],spd));
                            }
                    }
                    swap(pp[sps],pp[spd]);
                }
            }
        }
        q.pop();
    }
    if(memo.count(final) == 0) return "NA";
    if(memo[final] >= 21) return "NA";

    stringstream ss;
    ss << memo[final];

    return ss.str();
}

int main(void){
    mktbl();
    int n,m;
    while(cin >> n && n != -1){
        obj o;
        o[0] = n;
        REP(i,3){ cin >> m; o[i+1] = m; }
        REP(i,5){ cin >> m; o[i+4] = m; }
        REP(i,3){ cin >> m; o[i+9] = m; }
        cin >> m; o[12] = m;
        cout << solve(o) << endl;
    }
    return 0;
}