////////////////////
///   template   ///
////////////////////

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <functional>
#include <vector>
#include <queue>
#include <string>
#include <complex>
#include <stack>
#include <set>
#include <map>
#include <list>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
using namespace std;

//// MACRO ////
#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (s); i < (n); i++)
#define allof(c) c.begin(), c.end()
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)
#define EPS 1e-10
#define INF 1000000000

#define countof(a) (sizeof(a)/sizeof(a[0]))
#define PREDIACTE(t,a) [](const t & a) -> bool
#define COMPARISON_T(t) bool(*)(const t &, const t &)
#define COMPARISON(t,a,b) [](const t & a, const t & b) -> bool

//// prime ////
vector<unsigned char> isPrime;
vector<int> primes;
void initPrimes(int n)
{
	isPrime = vector<unsigned char>(n + 1, true);
	isPrime[0] = isPrime[1] = false;
	FOR(i, 2, n + 1)
	{
		if (!isPrime[i]) continue;
		primes.push_back(i);
		for (int j = i * 2; j <= n; j += i)
			isPrime[j] = false;
	}
}

//// Probability ////

// パスカルの三角形(二項定理) 2種類の並べ替えにつかう。
vector<vector<double>> makePascalTriangle(int n, bool probability = false)
{
	typedef vector<double> VD;
	vector<VD> t;
	if (!t.size()) { t.push_back(VD(1, 1)); }
	FOR(i, t.size(), n + 1)
	{
		t.push_back(VD(i + 1));
		REP(j, i)
		{
			double x = t[i - 1][j] * (probability ? 0.5 : 1);
			t[i][j] += x;
			t[i][j + 1] += x;
		}
	}
	return t;
}


//// iota iterator ////
struct iotait
{
	int n;
	iotait(int n = 0) : n(n) { }
	iotait &operator ++() { ++n; return *this; }
	int operator *() { return n; }
};

//// geo ////
struct P3
{
	double x, y, z;
	P3(double x = 0, double y = 0, double z = 0) : x(x), y(y), z(z) { }
	P3 operator +() const { return *this; }
	P3 operator +(const P3 &_) const { return P3(x + _.x, y + _.y, z + _.z); }
	P3 operator -() const { return P3(-x, -y, -z); }
	P3 operator -(const P3 &_) const { return *this + -_; }
	P3 operator *(double _) const { return P3(x*_, y*_, z*_); }
	P3 operator /(double _) const { return P3(x / _, y / _, z / _); }
	double dot(const P3 &_) const { return x*_.x + y*_.y + z*_.z; } // 内積
	P3 cross(const P3 &_) const { return P3(y*_.z - z*_.y, z*_.x - x*_.z, x*_.y - y*_.x); } // 外積
	double sqlength() const { return x*x + y*y + z*z; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P3 direction() const { return *this / length(); } // 方向ベクトル
};

struct Sphere
{
	P3 c;
	double r;
	Sphere(double x, double y, double z, double r) : c(x, y, z), r(r) { }
	bool IntersectWith(const Sphere &rhs) { return (c - rhs.c).length() - (r + rhs.r) < EPS; } // 接してても真。
};

//// bit ////
#ifdef _MSC_VER
inline unsigned __builtin_ctz(unsigned x) { unsigned long r; _BitScanForward(&r, x); return r; }
#endif

inline int next_bit_permutation(int x)
{
	int t = x | (x - 1);
	return (t + 1) | (unsigned)((~t & -~t) - 1) >> (__builtin_ctz(x) + 1);
}

//// graph ////
struct Path
{
	int from;
	int to;
	double cost;
	Path(int from = 0, int to = 0, double cost = 0) : from(from), to(to), cost(cost) { }
	bool operator < (const Path &rhs) const { return cost < rhs.cost; }
	bool operator >(const Path &rhs) const { return cost > rhs.cost; }
};



// prim //
pair<double, vector<int>> prim(const vector<vector<double>> &costTable)
{
	int N = costTable.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(0, 0, 0));

	vector<int> parent(N, -1);
	double totalCost = 0;
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (parent[i] != -1) continue;
		parent[i] = cur.from;
		totalCost += cur.cost;
		REP(j, N) if (parent[j] == -1) q.push(Path(i, j, costTable[i][j]));
	}
	return make_pair(totalCost, parent);
}

// dijkstra //
pair<vector<double>, vector<int>> dijkstra(const vector<vector<Path>> &routes, int start = 0, int goal = -1)
{
	int N = routes.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(start, start, 0));

	vector<int> prev(N, -1);
	vector<double> cost(N, INF);
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (prev[i] != -1) continue;
		prev[i] = cur.from;
		cost[i] = cur.cost;
		if (i == goal) { break; }
		REP(j, routes[i].size())
		{
			Path next = Path(i, routes[i][j].to, cur.cost + routes[i][j].cost);
			if (prev[next.to] == -1)
				q.push(next);
		}
	}
	return make_pair(cost, prev);
}

//// i/o ////
template <class T>
class vevector : public vector<vector<T>>
{
public:
	vevector(int n = 0, int m = 0) : vector<vector<T>>(n, vector<T>(m)) { };
	vevector(int n, int m, const T &initial) : vector<vector<T>>(n, vector<T>(m, initial)) { };
};

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(read<T>(read<int>())); return v; }
template <class T> void write(const T &t) { cout << t << endl; }
template <class T> void write(const T &t, const T &t2) { cout << t << ' ' << t2 << endl; }
template <class T> void write(const vector<T> &v)
{
	ostringstream ss;
	for (auto x : v) ss << x << ' ';
	auto s = ss.str();
	cout << s.substr(0, s.length() - 1) << endl;
}

struct _Reader { template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
#define READ(t,...) t __VA_ARGS__; _Reader(), __VA_ARGS__

template <class InIt1, class InIt2>
int partial_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2)
{
	return lexicographical_compare(first1, last1, first2, last2) ? -1
		: lexicographical_compare(first2, last2, first1, last1) ? 1
		: 0;
}

//// start up ////
void solve();
int main()
{
	// freopen("A.in", "r", stdin);
	solve();
	return 0;
}

////////////////////
/// template end ///
////////////////////

void dump(unsigned char *pv)
{
	REP(i, 4)
	{
		write(vector<int>(pv + i * 8, pv + i * 8 + 8));
	}
	write("");
}


void solve()
{
	int FREE = 0;

	union BD
	{
		unsigned char stt[32];
		unsigned long long ull[4];
		inline bool operator < (const BD &rhs) const { return lexicographical_compare(ull, ull + 4, rhs.ull, rhs.ull + 4); }
		inline bool operator ==(const BD &rhs) const { return equal(ull, ull + 4, rhs.ull); }
		static BD fromVector(const vector<int> &v) { BD r = {}; copy_n(v.begin(), 32, r.stt); return r; }
		struct hash { size_t operator() (const BD &b) const { return b.ull[0] ^ b.ull[1] ^ b.ull[2] ^ b.ull[3]; } };
	};

	BD goal;
	{
		vector<int> goal_;
		FOR(i, 1, 5) { FOR(j, 1, 8) goal_.push_back(i * 10 + j); goal_.push_back(FREE); }
		goal = BD::fromVector(goal_);
	}

	auto testcases = read<int>();
	REP(testcase, testcases)
	{

		BD initial;
		{
			vector<int> table = read<int>(28);
			table.insert(table.begin() + 0, FREE);
			table.insert(table.begin() + 8, FREE);
			table.insert(table.begin() + 16, FREE);
			table.insert(table.begin() + 24, FREE);

			swap(*find(allof(table), 11), table[0]);
			swap(*find(allof(table), 21), table[8]);
			swap(*find(allof(table), 31), table[16]);
			swap(*find(allof(table), 41), table[24]);

			initial = BD::fromVector(table);
		}

		auto visited = unordered_set<BD, BD::hash>();
		
		int result = -1;

		struct Node { BD bd; int step; };
		queue<Node> q;
		q.push({ initial, 0 });
		while (!q.empty())
		{
			Node cur = q.front(); q.pop();
			if (visited.count(cur.bd) > 0) { continue; }
			visited.insert(cur.bd);
			//dump(cur.bd.stt);

			if (cur.bd == goal) { result = cur.step; break; }
			REP(i, 4)
			{
				BD next = cur.bd;
				auto it = next.stt;
				REP(j, i + 1) it = find(it + 1, next.stt + 32, FREE);
				auto it2 = find(next.stt, next.stt + 32, *(it - 1) + 1);
				if (it2 != next.stt + 32)
				{
					swap(*it, *it2);
					if (visited.count(next) == 0) q.push({ next, cur.step + 1 });
				}
			}
		}

		write(result);
	}

}
### Prompt

Create a solution in cpp for the following problem:

Let’s play a card game called Gap.

You have 28 cards labeled with two-digit numbers. The first digit (from 1 to 4) represents the suit of the card, and the second digit (from 1 to 7) represents the value of the card.

First, you shuffle the cards and lay them face up on the table in four rows of seven cards, leaving a space of one card at the extreme left of each row. The following shows an example of initial layout.

<image>

Next, you remove all cards of value 1, and put them in the open space at the left end of the rows: “11” to the top row, “21” to the next, and so on.

Now you have 28 cards and four spaces, called gaps, in four rows and eight columns. You start moving cards from this layout.

<image>

At each move, you choose one of the four gaps and fill it with the successor of the left neighbor of the gap. The successor of a card is the next card in the same suit, when it exists. For instance the successor of “42” is “43”, and “27” has no successor.

In the above layout, you can move “43” to the gap at the right of “42”, or “36” to the gap at the right of “35”. If you move “43”, a new gap is generated to the right of “16”. You cannot move any card to the right of a card of value 7, nor to the right of a gap.

The goal of the game is, by choosing clever moves, to make four ascending sequences of the same suit, as follows.

<image>

Your task is to find the minimum number of moves to reach the goal layout.



Input

The input starts with a line containing the number of initial layouts that follow.

Each layout consists of five lines - a blank line and four lines which represent initial layouts of four rows. Each row has seven two-digit numbers which correspond to the cards.

Output

For each initial layout, produce a line with the minimum number of moves to reach the goal layout. Note that this number should not include the initial four moves of the cards of value 1. If there is no move sequence from the initial layout to the goal layout, produce “-1”.

Example

Input

4

12 13 14 15 16 17 21
22 23 24 25 26 27 31
32 33 34 35 36 37 41
42 43 44 45 46 47 11

26 31 13 44 21 24 42
17 45 23 25 41 36 11
46 34 14 12 37 32 47
16 43 27 35 22 33 15

17 12 16 13 15 14 11
27 22 26 23 25 24 21
37 32 36 33 35 34 31
47 42 46 43 45 44 41

27 14 22 35 32 46 33
13 17 36 24 44 21 15
43 16 45 47 23 11 26
25 37 41 34 42 12 31


Output

0
33
60
-1

### Response

```cpp
////////////////////
///   template   ///
////////////////////

#include <cstdio>
#include <cstring>
#include <cmath>
#include <iostream>
#include <sstream>
#include <algorithm>
#include <numeric>
#include <functional>
#include <vector>
#include <queue>
#include <string>
#include <complex>
#include <stack>
#include <set>
#include <map>
#include <list>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
using namespace std;

//// MACRO ////
#define REP(i,n) for (int i = 0; i < (n); i++)
#define RREP(i,n) for (int i = (n)-1; i >= 0; i--)
#define FOR(i,s,n) for (int i = (s); i < (n); i++)
#define allof(c) c.begin(), c.end()
#define partof(c,i,n) c.begin() + (i), c.begin() + (i) + (n)
#define EPS 1e-10
#define INF 1000000000

#define countof(a) (sizeof(a)/sizeof(a[0]))
#define PREDIACTE(t,a) [](const t & a) -> bool
#define COMPARISON_T(t) bool(*)(const t &, const t &)
#define COMPARISON(t,a,b) [](const t & a, const t & b) -> bool

//// prime ////
vector<unsigned char> isPrime;
vector<int> primes;
void initPrimes(int n)
{
	isPrime = vector<unsigned char>(n + 1, true);
	isPrime[0] = isPrime[1] = false;
	FOR(i, 2, n + 1)
	{
		if (!isPrime[i]) continue;
		primes.push_back(i);
		for (int j = i * 2; j <= n; j += i)
			isPrime[j] = false;
	}
}

//// Probability ////

// パスカルの三角形(二項定理) 2種類の並べ替えにつかう。
vector<vector<double>> makePascalTriangle(int n, bool probability = false)
{
	typedef vector<double> VD;
	vector<VD> t;
	if (!t.size()) { t.push_back(VD(1, 1)); }
	FOR(i, t.size(), n + 1)
	{
		t.push_back(VD(i + 1));
		REP(j, i)
		{
			double x = t[i - 1][j] * (probability ? 0.5 : 1);
			t[i][j] += x;
			t[i][j + 1] += x;
		}
	}
	return t;
}


//// iota iterator ////
struct iotait
{
	int n;
	iotait(int n = 0) : n(n) { }
	iotait &operator ++() { ++n; return *this; }
	int operator *() { return n; }
};

//// geo ////
struct P3
{
	double x, y, z;
	P3(double x = 0, double y = 0, double z = 0) : x(x), y(y), z(z) { }
	P3 operator +() const { return *this; }
	P3 operator +(const P3 &_) const { return P3(x + _.x, y + _.y, z + _.z); }
	P3 operator -() const { return P3(-x, -y, -z); }
	P3 operator -(const P3 &_) const { return *this + -_; }
	P3 operator *(double _) const { return P3(x*_, y*_, z*_); }
	P3 operator /(double _) const { return P3(x / _, y / _, z / _); }
	double dot(const P3 &_) const { return x*_.x + y*_.y + z*_.z; } // 内積
	P3 cross(const P3 &_) const { return P3(y*_.z - z*_.y, z*_.x - x*_.z, x*_.y - y*_.x); } // 外積
	double sqlength() const { return x*x + y*y + z*z; } // 二乗長さ
	double length() const { return sqrt(sqlength()); } // 長さ
	P3 direction() const { return *this / length(); } // 方向ベクトル
};

struct Sphere
{
	P3 c;
	double r;
	Sphere(double x, double y, double z, double r) : c(x, y, z), r(r) { }
	bool IntersectWith(const Sphere &rhs) { return (c - rhs.c).length() - (r + rhs.r) < EPS; } // 接してても真。
};

//// bit ////
#ifdef _MSC_VER
inline unsigned __builtin_ctz(unsigned x) { unsigned long r; _BitScanForward(&r, x); return r; }
#endif

inline int next_bit_permutation(int x)
{
	int t = x | (x - 1);
	return (t + 1) | (unsigned)((~t & -~t) - 1) >> (__builtin_ctz(x) + 1);
}

//// graph ////
struct Path
{
	int from;
	int to;
	double cost;
	Path(int from = 0, int to = 0, double cost = 0) : from(from), to(to), cost(cost) { }
	bool operator < (const Path &rhs) const { return cost < rhs.cost; }
	bool operator >(const Path &rhs) const { return cost > rhs.cost; }
};



// prim //
pair<double, vector<int>> prim(const vector<vector<double>> &costTable)
{
	int N = costTable.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(0, 0, 0));

	vector<int> parent(N, -1);
	double totalCost = 0;
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (parent[i] != -1) continue;
		parent[i] = cur.from;
		totalCost += cur.cost;
		REP(j, N) if (parent[j] == -1) q.push(Path(i, j, costTable[i][j]));
	}
	return make_pair(totalCost, parent);
}

// dijkstra //
pair<vector<double>, vector<int>> dijkstra(const vector<vector<Path>> &routes, int start = 0, int goal = -1)
{
	int N = routes.size();
	priority_queue<Path, vector<Path>, greater<Path>> q;
	q.push(Path(start, start, 0));

	vector<int> prev(N, -1);
	vector<double> cost(N, INF);
	while (!q.empty())
	{
		Path cur = q.top(); q.pop();
		int i = cur.to;
		if (prev[i] != -1) continue;
		prev[i] = cur.from;
		cost[i] = cur.cost;
		if (i == goal) { break; }
		REP(j, routes[i].size())
		{
			Path next = Path(i, routes[i][j].to, cur.cost + routes[i][j].cost);
			if (prev[next.to] == -1)
				q.push(next);
		}
	}
	return make_pair(cost, prev);
}

//// i/o ////
template <class T>
class vevector : public vector<vector<T>>
{
public:
	vevector(int n = 0, int m = 0) : vector<vector<T>>(n, vector<T>(m)) { };
	vevector(int n, int m, const T &initial) : vector<vector<T>>(n, vector<T>(m, initial)) { };
};

template <class T> T read() { T t; cin >> t; return t; }
template <class T> vector<T> read(int n) { vector<T> v; REP(i, n) { v.push_back(read<T>()); } return v; }
template <class T> vevector<T> read(int n, int m) { vevector<T> v; REP(i, n) v.push_back(read<T>(m)); return v; }
template <class T> vevector<T> readjag(int n) { vevector<T> v; REP(i, n) v.push_back(read<T>(read<int>())); return v; }
template <class T> void write(const T &t) { cout << t << endl; }
template <class T> void write(const T &t, const T &t2) { cout << t << ' ' << t2 << endl; }
template <class T> void write(const vector<T> &v)
{
	ostringstream ss;
	for (auto x : v) ss << x << ' ';
	auto s = ss.str();
	cout << s.substr(0, s.length() - 1) << endl;
}

struct _Reader { template <class T> _Reader operator ,(T &rhs) { cin >> rhs; return *this; } };
#define READ(t,...) t __VA_ARGS__; _Reader(), __VA_ARGS__

template <class InIt1, class InIt2>
int partial_compare(InIt1 first1, InIt1 last1, InIt2 first2, InIt2 last2)
{
	return lexicographical_compare(first1, last1, first2, last2) ? -1
		: lexicographical_compare(first2, last2, first1, last1) ? 1
		: 0;
}

//// start up ////
void solve();
int main()
{
	// freopen("A.in", "r", stdin);
	solve();
	return 0;
}

////////////////////
/// template end ///
////////////////////

void dump(unsigned char *pv)
{
	REP(i, 4)
	{
		write(vector<int>(pv + i * 8, pv + i * 8 + 8));
	}
	write("");
}


void solve()
{
	int FREE = 0;

	union BD
	{
		unsigned char stt[32];
		unsigned long long ull[4];
		inline bool operator < (const BD &rhs) const { return lexicographical_compare(ull, ull + 4, rhs.ull, rhs.ull + 4); }
		inline bool operator ==(const BD &rhs) const { return equal(ull, ull + 4, rhs.ull); }
		static BD fromVector(const vector<int> &v) { BD r = {}; copy_n(v.begin(), 32, r.stt); return r; }
		struct hash { size_t operator() (const BD &b) const { return b.ull[0] ^ b.ull[1] ^ b.ull[2] ^ b.ull[3]; } };
	};

	BD goal;
	{
		vector<int> goal_;
		FOR(i, 1, 5) { FOR(j, 1, 8) goal_.push_back(i * 10 + j); goal_.push_back(FREE); }
		goal = BD::fromVector(goal_);
	}

	auto testcases = read<int>();
	REP(testcase, testcases)
	{

		BD initial;
		{
			vector<int> table = read<int>(28);
			table.insert(table.begin() + 0, FREE);
			table.insert(table.begin() + 8, FREE);
			table.insert(table.begin() + 16, FREE);
			table.insert(table.begin() + 24, FREE);

			swap(*find(allof(table), 11), table[0]);
			swap(*find(allof(table), 21), table[8]);
			swap(*find(allof(table), 31), table[16]);
			swap(*find(allof(table), 41), table[24]);

			initial = BD::fromVector(table);
		}

		auto visited = unordered_set<BD, BD::hash>();
		
		int result = -1;

		struct Node { BD bd; int step; };
		queue<Node> q;
		q.push({ initial, 0 });
		while (!q.empty())
		{
			Node cur = q.front(); q.pop();
			if (visited.count(cur.bd) > 0) { continue; }
			visited.insert(cur.bd);
			//dump(cur.bd.stt);

			if (cur.bd == goal) { result = cur.step; break; }
			REP(i, 4)
			{
				BD next = cur.bd;
				auto it = next.stt;
				REP(j, i + 1) it = find(it + 1, next.stt + 32, FREE);
				auto it2 = find(next.stt, next.stt + 32, *(it - 1) + 1);
				if (it2 != next.stt + 32)
				{
					swap(*it, *it2);
					if (visited.count(next) == 0) q.push({ next, cur.step + 1 });
				}
			}
		}

		write(result);
	}

}
```