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

using namespace std;

#define rep(i, n) for (int i = 0; i < int(n); ++i)

map<vector<int>, int> mp;

int main() {
  vector<int> v;
  v.push_back(0);
  v.push_back(1);
  v.push_back(2);
  v.push_back(3);
  v.push_back(4);
  v.push_back(5);
  v.push_back(6);
  v.push_back(7);
  v.push_back(8);
  v.push_back(9);
  v.push_back(10);
  v.push_back(11);
  v.push_back(0);
  queue<pair<int, vector<int> > > que;
  que.push(make_pair(0, v));
  while (!que.empty()) {
    pair<int, vector<int> > now = que.front();
    que.pop();
    if (mp.count(now.second) != 0) continue;
    mp[now.second] = now.first;
    if (now.first == 10) continue;
    rep (i, 13) {
      if (now.second[i] != 0) continue;
      if (i == 0) {
	v = now.second;
	swap(v[0], v[2]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 1) {
	v = now.second;
	swap(v[1], v[2]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[1], v[5]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 2) {
	v = now.second;
	swap(v[2], v[0]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[2], v[1]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[2], v[3]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[2], v[6]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 3) {
	v = now.second;
	swap(v[3], v[2]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[3], v[7]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 4) {
	v = now.second;
	swap(v[4], v[5]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 5) {
	v = now.second;
	swap(v[5], v[1]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[5], v[4]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[5], v[6]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[5], v[9]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 6) {
	v = now.second;
	swap(v[6], v[2]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[6], v[5]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[6], v[7]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[6], v[10]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 7) {
	v = now.second;
	swap(v[7], v[3]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[7], v[6]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[7], v[8]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[7], v[11]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 8) {
	v = now.second;
	swap(v[8], v[7]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 9) {
	v = now.second;
	swap(v[9], v[5]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[9], v[10]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 10) {
	v = now.second;
	swap(v[10], v[6]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[10], v[9]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[10], v[11]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[10], v[12]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 11) {
	v = now.second;
	swap(v[11], v[7]);
	que.push(make_pair(now.first + 1, v));
	v = now.second;
	swap(v[11], v[10]);
	que.push(make_pair(now.first + 1, v));
      }
      if (i == 12) {
	v = now.second;
	swap(v[12], v[10]);
	que.push(make_pair(now.first + 1, v));
      }
    }
  }
  vector<int> p(13);
  for (;;) {
    cin >> p[0];
    if (p[0] == -1) break;
    rep (i, 12) cin >> p[i + 1];
    while (!que.empty()) que.pop();
    map<vector<int>, int> m;
    que.push(make_pair(0, p));
    bool find = false;
    while (!que.empty()) {
      pair<int, vector<int> > now = que.front();
      que.pop();
      if (mp.count(now.second) != 0) {
	cout << now.first + mp[now.second] << endl;
	find = true;
	break;
      }
      if (m.count(now.second) != 0) continue;
      m[now.second] = now.first;
      if (now.first == 10) continue;
      rep (i, 13) {
	if (now.second[i] != 0) continue;
	if (i == 0) {
	  v = now.second;
	  swap(v[0], v[2]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 1) {
	  v = now.second;
	  swap(v[1], v[2]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[1], v[5]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 2) {
	  v = now.second;
	  swap(v[2], v[0]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[2], v[1]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[2], v[3]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[2], v[6]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 3) {
	  v = now.second;
	  swap(v[3], v[2]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[3], v[7]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 4) {
	  v = now.second;
	  swap(v[4], v[5]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 5) {
	  v = now.second;
	  swap(v[5], v[1]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[5], v[4]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[5], v[6]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[5], v[9]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 6) {
	  v = now.second;
	  swap(v[6], v[2]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[6], v[5]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[6], v[7]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[6], v[10]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 7) {
	  v = now.second;
	  swap(v[7], v[3]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[7], v[6]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[7], v[8]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[7], v[11]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 8) {
	  v = now.second;
	  swap(v[8], v[7]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 9) {
	  v = now.second;
	  swap(v[9], v[5]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[9], v[10]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 10) {
	  v = now.second;
	  swap(v[10], v[6]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[10], v[9]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[10], v[11]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[10], v[12]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 11) {
	  v = now.second;
	  swap(v[11], v[7]);
	  que.push(make_pair(now.first + 1, v));
	  v = now.second;
	  swap(v[11], v[10]);
	  que.push(make_pair(now.first + 1, v));
	}
	if (i == 12) {
	  v = now.second;
	  swap(v[12], v[10]);
	  que.push(make_pair(now.first + 1, v));
	}
      }
    }
    if (!find) {
      cout << "NA" << endl;
    }
  }
  return 0;
}