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;

typedef long long ll;
typedef long double ld;
typedef tuple<int, int> duo;
const int dx[] = {0, 0, 1, -1, 1, 1, -1, -1};
const int dy[] = {1, -1, 0, 0, 1, -1, 1, -1};
const int Mod = 1000000000 + 0;
//{{{ templates
#define TT_             \
  template <typename T> \
  inline
#define TTF_                        \
  template <typename T, typename F> \
  inline
TT_ T sq(T x) { return x * x; }
TT_ T In() {
  T x;
  cin >> x;
  return x;
}
TT_ void Out(T& x) { cout << x; }
TT_ void sort(T& v) { sort(begin(v), end(v)); }
TT_ void revs(T& v) { reverse(begin(v), end(v)); }
TT_ void uniq(T& v) {
  sort(v);
  v.erase(unique(begin(v), end(v)), end(v));
}
TT_ int ubnd(T& v, typename T::value_type& x) {
  return upper_bound(begin(v), end(v), x) - begin(v);
}
TT_ int lbnd(T& v, typename T::value_type& x) {
  return lower_bound(begin(v), end(v), x) - begin(v);
}
TTF_ void inpt(T& v, int n, F f) {
  for (v.reserve(n); n--; v.emplace_back(f()))
    ;
}
TTF_ void show(T& v, F f, string d = " ", string e = "\n") {
  int i = 0;
  for (auto& x : v) i++&&(cout << d), f(x);
  cout << e;
}
TT_ typename T::iterator minel(T& v) { return min_element(begin(v), end(v)); }
TT_ typename T::iterator maxel(T& v) { return max_element(begin(v), end(v)); }

inline void fast_io() {
  ios::sync_with_stdio(0);
  cin.tie(0);
}
inline int in() {
  int x;
  scanf("%d", &x);
  return x;
}
inline ll pow_mod(ll a, ll k, ll m) {
  ll r = 1;
  for (; k > 0; a = a * a % m, k >>= 1)
    if (k & 1) r = r * a % m;
  return r;
}
inline ll mod_inv(ll a, ll p) { return pow_mod(a, p - 2, p); }
//}}} priority_queue queue deque front stringstream max_element min_element
// insert count make_tuple

struct Board {
  Board() {
    memcpy(b, "0123456789AB0", sizeof(b));
    find_zero();
  }
  Board(const vector<int>& v) {
    for (int i = 0; i < 13; i++) b[i] = conv_hex(v[i]);
    b[13] = 0;
    find_zero();
  }
  void find_zero(){
    int it = 0;
    for (int i = 0; i < 13; i++){
      if (b[i] == '0'){
        cur[it] = i;
        it++;
      }
    }
  }
  char conv_hex(int a) { return "0123456789ABCDEF"[a]; }
  bool slide(int index, int dir) {
    static const char mov[][4] = {
      {-1, -1, 2, -1},
      {-1, 2, 5, -1},
      {0, 3, 6, 1},
      {-1, -1, 7, 2},
      {-1, 5, -1, -1},
      {1, 6, 9, 4},
      {2, 7, 10, 5},
      {3, 8, 11, 6},
      {-1, -1, -1, 7},
      {5, 10, -1, -1},
      {6, 11, 12, 9},
      {7, -1, -1, 10},
      {10, -1, -1, -1},
    };
    char cu = cur[index];
    char nu = mov[cu][dir];
    if (nu == -1) return false;
    if (b[nu] == '0') return false;
    swap(b[cu], b[nu]);
    cur[index] = nu;
    turn++;
    return true;
  }
  char b[14];
  char cur[2];
  char turn;
};

int main() {
  unordered_map<ll, char> ans;
  Board b;
  queue<Board> Q;
  Q.push(b);
  while (!Q.empty()){
    Board bi = Q.front();
    Q.pop();
    ll hv = strtoll(bi.b, 0, 16);
    if (ans.count(hv)) continue;
    ans[hv] = bi.turn;
    if (bi.turn >= 20) continue;
    for (int i = 0; i < 2; i++){
      for (int d = 0; d < 4; d++){
        Board bii = bi;
        if (!bii.slide(i, d)) continue;
        Q.push(bii);
      }
    }
  }
  puts("END");
  int h;
  while (h = in(), h != -1) {
    vector<int> vs;
    vs.push_back(h);
    for (int i = 0; i < 12; i++) vs.push_back(in());
    Board b(vs);
    ll hv = strtoll(b.b, 0, 16);
    if (ans.count(hv)) cout << (int)ans[hv] << endl;
    else cout << "NA\n";
  }
  return 0;
}