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 <vector>
#include <algorithm>
#include <string>
#include <sstream>
#include <cstring>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <queue>
#include <stack>
#include <map>
#include <set>
#include <numeric>
#include <cctype>
#include <tuple>

#ifdef _MSC_VER
#include <agents.h>
#endif

#define FOR(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep(i, n) FOR(i, 0, n)
#define ALL(v) v.begin(), v.end()
#define REV(v) v.rbegin(), v.rend()
#define MEMSET(v, s) memset(v, s, sizeof(v))
#define X first
#define Y second

using namespace std;

typedef long long ll;
typedef pair<int, int> P;

const int N = 0;

inline int dist(int x1, int y1, int x2, int y2){
	return abs(x1 - x2) + abs(y1 - y2);
}

inline bool valid(int x, int y){
	return abs(x - 2) + abs(y - 2) <= 2;
}

void decode(ll x);

ll mov(ll state, int zero, int to){
	ll mask = 15ll << to*4;
	mask &= state;
	state ^= mask;
	int d = to - zero;
	if (d < 0) state |= mask << -d*4;
	else state |= mask >> d*4;
	return state;
}

void decode(ll x){
	vector<string> vs;
	rep(i, 5){
		string s;
		rep(j, 5){
			if (valid(j, i)){
				int tmp = x & 15;
				s += " ";
				s += '0' + tmp % 10;
				s += '0' + tmp / 10;
				x >>= 4;
			}
			else{
				s += " ..";
			}
		}
		vs.push_back(string(REV(s)));
	}
	reverse(ALL(vs));
	for (auto &s : vs){
		cout << s << endl;
	}
}

int mat[5][5];

struct state{
	ll enc;
	int d;
	int pos[2];
	state(ll e, int p0, int p1, int d) :enc(e), d(d){ pos[0] = p0, pos[1] = p1; };
};

int main(){

	int pos = 0;
	vector<vector<int>> adj;
	{
		int tmp = 0;
		rep(i, 5) rep(j, 5) if (valid(j, i)) mat[i][j] = tmp++;
	}
	rep(i, 5) rep(j, 5){
		vector<int> v;
		if (!valid(j, i)) continue;
		rep(k, 5) rep(l, 5){
			if (!valid(l, k)) continue;
			if (dist(j, i, l, k) != 1) continue;
			v.push_back(mat[k][l]);
		}
		adj.push_back(v);
	}

	ll init = 0;
	int tmp = 0;
	rep(i, 5) rep(j, 5){
		if (!valid(j, i)) continue;
		init <<= 4;
		init |= (tmp++) % 12;
	}

	map<ll, int> m;
	m[init] = 0;
	queue<state> q;
	q.push({ init, 0, 12, 0 });
	while (!q.empty()){
		state s = q.front();
		q.pop();

		rep(i, 2){
			for (auto to : adj[s.pos[i]]){
				ll nxt = mov(s.enc, s.pos[i], to);
				if (m.count(nxt)) continue;
				m[nxt] = s.d + 1;
				if (s.d + 1 < 10) q.push({ nxt, s.pos[!i], to, s.d + 1 });
			}
		}
	}

	ll x;
	while (cin >> x, ~x){
		vector<int> zero;
		int in;
		rep(i, 12){
			cin >> in;
			x = (x << 4) + in;
			if (!in) zero.push_back(i + 1);
		}
		if (zero.size() <= 1) zero.push_back(0);
		//decode(x);

		set<ll> vis;
		queue<state> q;
		q.push({ x, zero[0], zero[1], 0 });
		int ans = -1;
		if (m.count(x)){
			ans = m[x];
		}
		else
		while (!q.empty()){
			state s = q.front();
			q.pop();

			rep(i, 2){
				for (auto to : adj[s.pos[i]]){
					ll nxt = mov(s.enc, s.pos[i], to);
					if (vis.count(nxt)) continue;
					vis.insert(nxt);
					if (m.count(nxt)){
						ans = s.d + m[nxt] + 1;
						goto end;
					}
					if (s.d + 1 < 10) q.push({ nxt, s.pos[!i], to, s.d + 1 });
				}
			}
		}
end:
		if (ans >= 0) cout << ans << endl;
		else cout << "NA" << endl;
	}


	return 0;
}