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>

#define fst(t) std::get<0>(t)
#define snd(t) std::get<1>(t)
#define thd(t) std::get<2>(t)
#define unless(p) if(!(p))
#define until(p) while(!(p))

using ll = std::int64_t;
using P = std::tuple<int,int>;

const int dx[4] = {-1, 1, 0, 0}, dy[4] = {0, 0, -1, 1};

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

int gX[12], gY[12];

inline int f(int y, int x, int p){
    if(p > 0){
        return dist(y, x, gY[p], gX[p]);
    }
    return 0;
}

struct Puzzle{
    std::vector<char> board;
    std::vector<P> spaces;
    int estimatedDist;
    ll id;

    Puzzle() : board(25, 0), spaces(2), estimatedDist(0), id(0) { 
        for(int i=1;i<=11;++i){
            if(i <= 3){
                at(1, i) = i;
            }else if(i <= 8){
                at(2, i - 4) = i;
            }else{
                at(3, i - 8) = i;
            }
        }

        for(int i=0;i<5;++i){
            for(int j=0;j<5;++j){
                estimatedDist += f(i, j, at(i, j));
                if(at(i, j) > 0){
                    id |= ((5ll * i + j) << (5 * at(i, j)));
                }
            }
        }

        spaces[0] = std::make_tuple(0, 2);
        spaces[1] = std::make_tuple(4, 2);
    }

    void move(int spaceId, int y, int x){        
        int sX, sY;
        std::tie(sY, sX) = spaces[spaceId];

        estimatedDist += - f(y, x, at(y, x)) + f(sY, sX, at(y, x));
        id ^= ((5ll * y + x) ^ (5ll * sY + sX)) << (5 * at(y, x));
        at(sY, sX) = at(y, x);
        at(y, x) = 0;
        spaces[spaceId] = std::make_tuple(y, x);
    }

    char& at(int y, int x){
        return board[y * 5 + x];
    }
};

struct State{
    int turn;
    Puzzle puzzle;

    State(int t, Puzzle p) : turn(t), puzzle(std::move(p)) {}

    friend bool operator>(const State &lhs, const State &rhs){
        return lhs.turn + lhs.puzzle.estimatedDist > rhs.turn + rhs.puzzle.estimatedDist;
    }
};

std::map<ll, int> minDist;
std::priority_queue<State, std::vector<State>, std::greater<State>> pq;

int solve(){
    minDist.clear();
    until(pq.empty()){
        pq.pop();
    }

    Puzzle initialPuzzle;
    pq.emplace(0, initialPuzzle);
    minDist[initialPuzzle.id] = 0;

    until(pq.empty()){
        State s = pq.top();
        pq.pop();

        if(s.puzzle.estimatedDist == 0){
            return s.turn;
        }

        if(s.turn + s.puzzle.estimatedDist > 20 ||
           s.turn > minDist[s.puzzle.id]){
            continue;
        }

        for(int i=0;i<2;++i){
            for(int j=0;j<4;++j){
                int x, y;
                std::tie(y, x) = s.puzzle.spaces[i];

                y += dy[j];
                x += dx[j];

                if(dist(y, x, 2, 2) > 2 || s.puzzle.at(y, x) == 0){
                    continue;
                }

                Puzzle p = s.puzzle;
                p.move(i, y, x);

                if(minDist.count(p.id) == 0 || minDist[p.id] > s.turn + 1){
                    minDist[p.id] = s.turn + 1;
                    pq.emplace(s.turn + 1, p);
                }
            }
        }
    }

    return -1;
}

int main(){
    std::cin.tie(nullptr);
    std::ios::sync_with_stdio(false);

    while(true){
        for(int i=0;i<5;++i){
            for(int j=0;j<5;++j){
                if(dist(i, j, 2, 2) > 2){
                    continue;
                }

                int p;
                std::cin >> p;

                if(p == -1){
                    return 0;
                }

                gY[p] = i;
                gX[p] = j;
            }
        }

        int mn = solve();
        if(mn >= 0){
            std::cout << mn << std::endl;
        }else{
            std::cout << "NA" << std::endl;
        }
    }
}