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<algorithm>
#include<iomanip>

#define N 7
#define INV (-1)

#define UP 0
#define RIGHT 1
#define DOWN 2
#define LEFT 3
#define DIRMAX 4

#define NA 20

using namespace std;

struct State
{
  int map[N][N];
  State(){
    //fill(&map[0][0],&map[N-1][N-1],-1);
  }
  State(int tmap[][N]){
    for(int i = 0; i < N; ++i){
      for(int j = 0; j < N; ++j){
	map[i][j] = tmap[i][j];
      }
    }
  }
  bool move(int which, int dir){
    // which = 0, upper,left
    // which != 0, bottom,right
    for(int i = (which==0?0:N-2); which==0?(i<N-1):(i>=1); which==0?++i:--i){
      for(int j = (which==0?0:N-2); which==0?(j<N-1):(j>=1); which==0?++j:--j){
	if( map[i][j] == 0 ){
	  switch(dir){
	  case UP:   if( map[i-1][j] > 0 ){swap( map[i][j], map[i-1][j] );return true;}break;
	  case RIGHT:if( map[i][j+1] > 0 ){swap( map[i][j], map[i][j+1] );return true;}break;
	  case DOWN: if( map[i+1][j] > 0 ){swap( map[i][j], map[i+1][j] );return true;}break;
	  case LEFT: if( map[i][j-1] > 0 ){swap( map[i][j], map[i][j-1] );return true;}break;
	  }
	  return false;
	}
      }
    }
  }
  int getHeuristic()const{
    const int ti[] = {0,2,2,2,3,3,3,3,3,4,4,4};
    const int tj[] = {0,2,3,4,1,2,3,4,5,2,3,4};
    int ret = 0;
    int max1=0,max2=0;
    for(int i = 1; i < N-1; ++i){
      for(int j = 1; j < N-1; ++j){
	if( map[i][j] > 0 ){
	  int x = abs(i-ti[map[i][j]] )+ abs(j-tj[map[i][j]]);
	  ret += x;
	  if( max1 < x ){
	    max2 = max1;
	    max1 = x;
	  }
	}
      }
    }
    return ret;
  }
  bool isComplete()const{
    return getHeuristic() == 0;
  }
};

int IterativeDeepning(int depth, const State &now, int &ans)
{

  if( now.isComplete() ){
    ans = min( ans , depth );
    return ans;
  }
  int least = depth+now.getHeuristic();
  if( least > ans ){
    return NA;
  }
  // ans = min( ans, least );
  for(int w = 0; w < 2; ++w){
    for(int dir = 0; dir < DIRMAX; ++dir){
      State next = now;
      if( next.move( w, dir ) ){
	ans = min( ans, IterativeDeepning( depth + 1, next, ans ) );
      }
    }
  }
  return NA;
}

int main()
{
  while(true){
    int map[N][N];
    int ans;
    fill(&map[0][0],&map[N-1][N],-1);
    
    const int imax[] = {1,3,5,3,1};
    const int dj[] = {2,1,0,1,2};
    for(int i = 0; i < 5; ++i){
      for(int j = 0; j < imax[i]; ++j){
	int t;
	cin >> t;
	if( t < 0 ) return 0;
	map[i+1][j+dj[i]+1]=t;
      }
    }

    /*
    for(int i = 0; i < N; ++i){
      for(int j = 0; j < N; ++j){
	cout << setw(3) << map[i][j] << ' ';
      }
      cout << endl;
    }
    cout << endl;
    */

    ans = NA;
    IterativeDeepning( 0, State(map), ans );
    if( ans > NA ){
      cout << "NA" << endl;
    }else{
      cout << ans << endl;
    }
      
  }
  return 0;
}