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<cstdio>
using namespace std;
int field[5][5];
int log[5][5];
int num[13];
void SETING();
int main(){
  while(cin >>num[0]){
    if(num[0] == -1){break;}
    int a;
    for(int i=1; i<13; i++){
      cin >>a;
      num[i] = a;
    }
    SETING();
    int cost = 0;
    for(int k=1; k<12; k++){
      int x,y,s,t;
      for(int i=0; i<5; i++){
	for(int j=0; j<5; j++){
	  if(field[i][j] == k){x = i; y = j;}
	}
      }
      for(int i=0; i<5; i++){
	for(int j=0; j<5; j++){
	  if(log[i][j] == k){s = i; t = j;}
	}
      }
      if(x>s){cost+=x-s;}
      if(x<s){cost+=s-x;}
      if(y>t){cost+=y-t;}
      if(y<t){cost+=t-y;}
    }
    if(cost<21){cout <<cost<<endl;}
    else{cout <<"NA"<<endl;}
  }
  return 0;
}
void SETING(){
  for(int i=0; i<5; i++){
    for(int j=0; j<5; j++){
      field[i][j] = -1;
      log[i][j] = -1;
    }
  }
  field[2][0] = num[0];
  field[1][1] = num[1];
  field[2][1] = num[2];
  field[3][1] = num[3];
  field[1][2] = num[4];
  field[1][2] = num[5];
  field[2][2] = num[6];
  field[3][2] = num[7];
  field[4][2] = num[8];
  field[1][3] = num[9];
  field[2][3] = num[10];
  field[3][3] = num[11];
  field[2][4] = num[12];
  log[2][0] = 0;
  log[1][1] = 1;
  log[2][1] = 2;
  log[3][1] = 3;
  log[1][2] = 4;
  log[1][2] = 5;
  log[2][2] = 6;
  log[3][2] = 7;
  log[4][2] = 8;
  log[1][3] = 9;
  log[2][3] = 10;
  log[3][3] = 11;
  log[2][4] = 0;
}

C++: #include <iostream>
#include <iomanip>
#include <vector>
#include <map>
#include <set>
#include <queue>
using namespace std;

#define NONE -1

// »ÝÌóÔ
vector < vector <int> > F( 5, vector <int>(5,NONE) );
// S[
vector < vector <int> > GOAL( 5, vector <int>(5,NONE) );
// KâÏÝ
set < vector < vector <int> > > V;
// ó«Ìê
int empty_x[2];
int empty_y[2];
int now;

int abs( int n )
{
	if ( n < 0 )
		return -n;
	return n;
}

int getMD()
{
	int md = 0;
	for ( int i = 0; i < 5; i++ ) for ( int j = 0; j < 5; j++ )
	{
		if ( F[i][j] != GOAL[i][j] )
		{
			// T·
			bool found = false;
			for ( int k = 0; k < 5; k++ )
			{
				for ( int m = 0; m < 5; m++ )
				{
					//  Á½
					if ( F[i][j] == GOAL[k][m] )
					{
						md += abs(k-i) + abs(m-j);
						found = true;
						break;
					}
				}
				if ( found ) break;
			}
		}
	}
	return md;
}

bool search( int depth )
{
	if ( F == GOAL )
		return true;
	if ( now + getMD() > depth )
		return false;

	now++;
	for ( int e = 0; e < 2; e++ ) for ( int i = -1; i < 2; i++ ) for ( int j = -1; j < 2; j++ )
	{
		if ( i+j == 1 || i+j == -1 )
		{
			int ox = empty_x[e];
			int oy = empty_y[e];
			int tx = empty_x[e] + i;
			int ty = empty_y[e] + j;

			if ( ( tx >= 0 && tx <= 4 ) && ( ty >= 0 && ty <= 4 ) )
			{
				if ( F[ty][tx] != 0 && F[ty][tx] != NONE )
				{
					// ®©·
					swap( F[oy][ox], F[ty][tx] );

					// ¢JÌnÅ éÈçÎ
					if ( V.find( F ) == V.end() )
					{
						if ( search( depth ) )
							return true;
					}

					// ß·
					swap( F[oy][ox], F[ty][tx] );
				}
			}
		}
	}
	now--;

}

int main( void )
{
	while ( 1 )
	{
		// S[ðìé
		GOAL[0][2] = 0;
		for ( int i = 0; i < 3; i++ )
			GOAL[1][1+i] = i+1;
		for ( int i = 0; i < 5; i++ )
			GOAL[2][i] = 4 + i;
		for ( int i = 0; i < 3; i++ )
			GOAL[3][1+i] = 9 + i;
		GOAL[4][2] = 0;

		// üÍ
		cin >> F[0][2];
		if ( F[0][2] == -1 )
			break;
		for ( int i = 0; i < 3; i++ )
			cin >> F[1][1+i];
		for ( int i = 0; i < 5; i++ )
			cin >> F[2][i];
		for ( int i = 0; i < 3; i++ )
			cin >> F[3][1+i];
		cin >> F[4][2];

		// óðT·
		int empty_count = 0;
		for ( int i = 0; i < 5; i++ )
		{
			for ( int j = 0; j < 5; j++ )
			{
				if ( F[i][j] == 0 )
				{
					empty_x[empty_count] = j;
					empty_y[empty_count] = i;
					empty_count++;
				}
			}
		}

		// ½[»[³DæTõ
		V.insert( F );
		now = 0;
		bool goal_flag = false;
		for ( int i = 0; i <= 20; i++ )
		{
			if ( search( i ) )
			{
				goal_flag = true;
				break;
			}
		}

		if ( goal_flag )
			cout << now << endl;
		else
			cout << "NA" << endl;

	}
	return 0;
}