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 <bits/stdc++.h>

using namespace std;

#define LIMIT 20

struct P{
  int y,x;
  P(int y,int x) : y(y),x(x) {}
};

int limit;
vector<int> v;

P getPos(int x){
  if(x == 0){ return P(0,2); }
  if(1 <= x && x <= 3){ return P(1,x); }
  if(4 <= x && x <= 8){ return P(2,x-4); }
  if(9 <= x && x <= 11){ return P(3,x-8); }
  return P(4,2);
}

int getPos(P p){
  if(p.y == 0){
    if(p.x == 2){ return 0; }
    else{ return -1; }
  }
  if(p.y == 1){
    if(1 <= p.x && p.x <= 3){
      return p.x;
    }else{
      return -1;
    }
  }
  if(p.y == 2){
    if(0 <= p.x && p.x <= 4){
      return p.x+4;
    }else{
      return -1;
    }
  }
  if(p.y == 3){
    if(1 <= p.x && p.x <= 3){
      return p.x+8;
    }else{
      return -1;
    }
  }
  if(p.y == 4){
    if(p.x == 2){
      return 12;
    }else{
      return -1;
    }
  }
  return -1;
}

int getMD(){
  int sum = 0;
  for(int i = 0 ; i < 13 ; i++){
    if(v[i] == 0){ continue; }
    P np = getPos(i);
    P tp = getPos(v[i]);
    sum += abs(np.x-tp.x) + abs(np.y-tp.y);
  }
  return sum;
}

const int dx[] = {-1,0,1,0};
const int dy[] = {0,-1,0,1};

bool dfs(int sp1,int sp2,int step){
  int md = getMD();
  if(md == 0){ return true; }
  if(md + step > limit){
    return false;
  }
  P p[2] = {getPos(sp1),getPos(sp2)};
  for(int i = 0 ; i < 2 ; i++){
    int x = p[i].x, y = p[i].y;
    for(int j = 0 ; j < 4 ; j++){
      int nx = x + dx[j], ny = y + dy[j];
      P np(ny,nx);
      int next = getPos(np);
      if(next == -1){ continue; }
      if(i == 0){
        swap(v[sp1],v[next]);
        if(dfs(next,sp2,step+1)){
          return true;
        }
        swap(v[sp1],v[next]);
      }else{
        swap(v[sp2],v[next]);
        if(dfs(sp1,next,step+1)){
          return true;
        }
        swap(v[sp2],v[next]);
      }
    }
  }
  return false;
}

int main(){
  int x;
  while(cin >> x, x != -1){
    int sp[2];
    v.resize(13); v[0] = x;
    for(int i = 1 ; i < 13 ; i++){
      cin >> v[i];
    }
    for(int i = 0, j = 0 ; i < 13 ; i++){
      if(v[i] == 0){
        sp[j++] = i;
      }
    }
    bool found = false;
    for(limit = 0 ; limit <= LIMIT ; limit++){
      if(dfs(sp[0],sp[1],0)){
        cout << limit << endl;
        found = true;
        break;
      }
    }
    if(!found){
      cout << "NA" << endl;
    }
  }
  return 0;
}