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 rep(i,n)for(int i=0;i<(n);i++)
using namespace std;

int cx[]{ 0,1,1,1,2,2,2,2,2,3,3,3,4 }, cy[]{ 2,1,2,3,0,1,2,3,4,1,2,3,2 };
int dx[]{ 1,-1,0,0 }, dy[]{ 0,0,1,-1 };
int d[5][5], lim, D, x[2], y[2];
bool dfs(int p) {
	if (D == 0)return true;
	if (p + D > lim)return false;
	rep(j, 2)rep(i, 4) {
		int nx = x[j] + dx[i], ny = y[j] + dy[i];
		if (nx < 0 || 5 <= nx || ny < 0 || 5 <= ny || !d[nx][ny])continue;
		int a = abs(cx[d[nx][ny]] - nx) + abs(cy[d[nx][ny]] - ny);
		int b = abs(cx[d[nx][ny]] - x[j]) + abs(cy[d[nx][ny]] - y[j]);
		D += b - a; swap(d[x[j]][y[j]], d[nx][ny]); swap(x[j], nx); swap(y[j], ny);
		if (dfs(p + 1))return true;
		D -= b - a; swap(d[x[j]][y[j]], d[nx][ny]); swap(x[j], nx); swap(y[j], ny);
	}
	return false;
}
int main() {
	while (1) {
		D = 0; int p = 0;
		rep(i, 13) {
			scanf("%d", &d[cx[i]][cy[i]]);
			if (d[cx[i]][cy[i]] == -1)return 0;
			if (d[cx[i]][cy[i]] == 0) {
				x[p] = cx[i]; y[p++] = cy[i];
			}
			else D += abs(cx[i] - cx[d[cx[i]][cy[i]]]) + abs(cy[i] - cy[d[cx[i]][cy[i]]]);
		}
		for (lim = 0; lim <= 20; lim++) {
			if (dfs(0)) {
				printf("%d\n", lim); break;
			}
		}
		if (lim == 21)puts("NA");
	}
}

C++: #include <iostream>
#include <sstream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <ctime>
#include <cstring>
#include <climits>
#include <algorithm>
#include <map>
#include <set>
#include <stack>
#include <vector>
#include <queue>
#include <bitset>
#include <string>
using namespace std;
 
#define rep(i,n) for(int i=0; i<n; i++)
#define repa(i,s,e) for(int i=s; i<=e; i++)
#define repd(i,s,e) for(int i=s; i>=e; i--)
#define PB(a) push_back(a)
#define MP(i,s) make_pair(i,s)
 
typedef long long ll;

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

const int field[5][5] = {
	{0, 0, 1, 0, 0}, 
	{0, 1, 1, 1, 0},
	{1, 1, 1, 1, 1},
	{0, 1, 1, 1, 0},
	{0, 0, 1, 0, 0}, 
};

const int ans[5][5] = {
	{0, 0, 0, 0, 0},
	{0, 1, 2, 3, 0},
	{4, 5, 6, 7, 8},
	{0, 9, 10, 11, 0},
	{0, 0, 0, 0, 0}
};

const int px[13] = {2, 1, 2, 3, 0, 1, 2, 3, 4, 1, 2, 3, 2};
const int py[13] = {0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4};

int P[5][5];
map<ll,int> used;
map<ll,int> H;

ll hash_val() {
	ll h = 0;
	rep(i,13) {
		h *= 13;
		h += P[py[i]][px[i]];
	}
	return h;
}

void make_ans(int m, int d) {
	ll h = hash_val();
	map<ll,int>::iterator it = H.find(h);
	
	if(it == H.end()) {
		H.insert(MP(h,m));
	} else if((*it).second > m) {
		(*it).second = m;
	} else {
		return;
	}

	if(m == d) return;


	rep(i,13) {
		int x = px[i];
		int y = py[i];
		if(P[y][x] == 0) {
			rep(k,4) {
				int xx = x + dx[k];
				int yy = y + dy[k];
				if(xx>=0 && yy>=0 && xx<5 && yy<5 && field[yy][xx] == 1 && P[yy][xx] != 0) {
					swap(P[y][x], P[yy][xx]);
					make_ans(m+1, d);
					swap(P[y][x], P[yy][xx]);
				}
			}
		}
	}
}

int dfs(int m, int d) {
	map<ll,int>::iterator it;
	ll h = hash_val();

	it = H.find(h);
	if(it != H.end()) return m + (*it).second;

	if(m == d) return -1;
	
	it = used.find(h);
	if(it == used.end()) {
		used.insert(MP(h,m));
	} else if((*it).second > m) {
		(*it).second = m;
	} else {
		return -1;
	}

	rep(i,13) {
		int x = px[i];
		int y = py[i];
		if(P[y][x] == 0) {
			rep(k,4) {
				int xx = x + dx[k];
				int yy = y + dy[k];
				if(xx>=0 && yy>=0 && xx<5 && yy<5 && field[yy][xx] == 1 && P[yy][xx] != 0) {
					swap(P[y][x], P[yy][xx]);
					int a = dfs(m+1, d);
					if(a >= 0) return a;
					swap(P[y][x], P[yy][xx]);
				}
			}
		}
	}
	return -1;
}

void solve() {
	repa(d,0,10) {
		used.clear();
		int a = dfs(0, d);
		if(a >= 0) {
			printf("%d\n", a);
			return;
		}
	}
	printf("NA\n");
}

int main() {
	memcpy(P, ans, sizeof(P));
	make_ans(0, 10);
	for(;;) {
		rep(i,13) {
			scanf("%d", &P[py[i]][px[i]]);
			if(P[py[i]][px[i]] < 0) return 0;
		}
		solve();
	}
}