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<iostream>
#include<vector>
#include<algorithm>
#include<map>
#include<queue>

using namespace std;

map<vector<int>,int>mp,used;

struct State{
  vector<int>v;
  int t;
  State(vector<int>v,int t):v(v),t(t){}
};

vector<vector<int> > generate(vector<int> v){
  vector<vector<int> >res;

  for(int i=0;i<13;i++){
    if(v[i]==0){
      vector<int>tmp=v;
      switch(i){
      case 0:
	swap(tmp[0],tmp[2]);
	res.push_back(tmp);
	break;
      case 1:
	swap(tmp[1],tmp[2]);
	res.push_back(tmp);
	swap(tmp[1],tmp[2]);
	swap(tmp[1],tmp[5]);
	res.push_back(tmp);
	break;
      case 2:
	swap(tmp[2],tmp[0]);
	res.push_back(tmp);
	swap(tmp[2],tmp[0]);

	swap(tmp[2],tmp[1]);
	res.push_back(tmp);
	swap(tmp[2],tmp[1]);

	swap(tmp[2],tmp[3]);
	res.push_back(tmp);
	swap(tmp[2],tmp[3]);

	swap(tmp[2],tmp[6]);
	res.push_back(tmp);
	break;
      case 3:
	swap(tmp[3],tmp[2]);
	res.push_back(tmp);
	swap(tmp[3],tmp[2]);

	swap(tmp[3],tmp[7]);
	res.push_back(tmp);
	break;
      case 4:
	swap(tmp[4],tmp[5]);
	res.push_back(tmp);
	break;
      case 5:
	swap(tmp[5],tmp[1]);
	res.push_back(tmp);
	swap(tmp[5],tmp[1]);

	swap(tmp[5],tmp[4]);
	res.push_back(tmp);
	swap(tmp[5],tmp[4]);

	swap(tmp[5],tmp[6]);
	res.push_back(tmp);
	swap(tmp[5],tmp[6]);

	swap(tmp[5],tmp[9]);
	res.push_back(tmp);
	break;
      case 6:
	swap(tmp[6],tmp[2]);
	res.push_back(tmp);
	swap(tmp[6],tmp[2]);

	swap(tmp[6],tmp[5]);
	res.push_back(tmp);
	swap(tmp[6],tmp[5]);

	swap(tmp[6],tmp[7]);
	res.push_back(tmp);
	swap(tmp[6],tmp[7]);

	swap(tmp[6],tmp[10]);
	res.push_back(tmp);
	break;
      case 7:
	swap(tmp[7],tmp[3]);
	res.push_back(tmp);
	swap(tmp[7],tmp[3]);

	swap(tmp[7],tmp[6]);
	res.push_back(tmp);
	swap(tmp[7],tmp[6]);

	swap(tmp[7],tmp[8]);
	res.push_back(tmp);
	swap(tmp[7],tmp[8]);

	swap(tmp[7],tmp[11]);
	res.push_back(tmp);
	break;
      case 8:
	swap(tmp[8],tmp[7]);
	res.push_back(tmp);
	break;
      case 9: 
	swap(tmp[9],tmp[5]);
	res.push_back(tmp);
	swap(tmp[9],tmp[5]);

	swap(tmp[9],tmp[10]);
	res.push_back(tmp);
	break;
      case 10:
	swap(tmp[10],tmp[6]);
	res.push_back(tmp);
	swap(tmp[10],tmp[6]);

	swap(tmp[10],tmp[9]);
	res.push_back(tmp);
	swap(tmp[10],tmp[9]);

	swap(tmp[10],tmp[11]);
	res.push_back(tmp);
	swap(tmp[10],tmp[11]);

	swap(tmp[10],tmp[12]);
	res.push_back(tmp);
	break;
      case 11:
	swap(tmp[11],tmp[7]);
	res.push_back(tmp);
	swap(tmp[11],tmp[7]);

	swap(tmp[11],tmp[10]);
	res.push_back(tmp);
	break;
      case 12:
	swap(tmp[12],tmp[10]);
	res.push_back(tmp);
	break;
      }
    }
  }
  return res;
}

void bfs(void){

  queue<State>que;
  vector<int>s;
  for(int i=0;i<12;i++)s.push_back(i);
  s.push_back(0);
  que.push(State(s,0));

  while(!que.empty()){
    State now=que.front();
    que.pop();
    
    if(mp.count(now.v) && now.t>=mp[now.v])continue;
    if(now.t>=12)continue;

    mp[now.v]=now.t;

    vector<vector<int> >res=generate(now.v);
    for(int i=0;i<res.size();i++){
      que.push(State(res[i],now.t+1));
    }
  }
}

int bfs(vector<int> s){
  
  used.clear();
  
  queue<State>que;
  que.push(State(s,0));
  
  while(!que.empty()){
    State now=que.front();
    que.pop();
    
    if(now.t>=11)continue;
    if(used.count(now.v))continue;
    if(mp.count(now.v))return now.t+mp[now.v];
    used[now.v]=1;
    
    vector<vector<int> >res=generate(now.v);
    for(int i=0;i<res.size();i++){
      que.push(State(res[i],now.t+1));
    }
  }
  return -1;
}

int main(void){

  bfs();

  while(true){
    vector<int>s(13);
    for(int i=0;i<13;i++){
      cin >> s[i];
      if(s[i]<0)return 0;
    }
    int res=bfs(s);
    if(res<0 || res>20)cout << "NA" << endl;
    else cout << res << endl;
  }

  return 0;
}