#include <bits/stdc++.h>
using namespace std;

using VI = vector<int>;
using VVI = vector<VI>;
using PII = pair<int, int>;
using LL = long long;
using VL = vector<LL>;
using VVL = vector<VL>;
using PLL = pair<LL, LL>;
using VS = vector<string>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

#define FF first
#define SS second
template<class S, class T>
istream& operator>>(istream& is, pair<S,T>& p){
  return is >> p.FF >> p.SS;
}
template<class S, class T>
ostream& operator<<(ostream& os, const pair<S,T>& p){
  return os << p.FF << " " << p.SS;
}
template<class T>
void maxi(T& x, T y){
  if(x < y) x = y;
}
template<class T>
void mini(T& x, T y){
  if(x > y) x = y;
}


const double EPS = 1e-10;
const double PI  = acos(-1.0);
const LL MOD = 1e9+7;

int H, W, N;
PII xs[18][500][500];

int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cin >> H >> W >> N;
  REP(y,H) REP(x,W)
	cin >> xs[0][y][x];

  vector<PII> ps(N);
  REP(i,N) cin >> ps[i];

  for(int i=1;i<18;++i){
	REP(y,H) REP(x,W){
	  auto&& par = xs[i-1][y][x];
	  xs[i][y][x] = xs[i-1][par.FF][par.SS];
	}
  }

  bool no = true;
  set<PII> s;
  for(auto&& p: ps){
	PII np = xs[17][p.FF][p.SS];
	if(s.count(np)){
	  no = false;
	}
	s.insert(np);
  }
  if(no){
	cout << -1 << endl;
	return 0;
  }

  int ans = 0;
  vector<vector<PII>> db(H, vector<PII>(W));
  REP(y,H) REP(x,W) db[y][x] = MP(y,x);
  for(int i=17;i>=0;--i){
	bool excess = false;
	set<PII> s;
	for(auto&& p: ps){
	  PII np = db[p.FF][p.SS];
	  np = xs[i][np.FF][np.SS];
	  if(s.count(np)){
		excess = true;
		break;
	  }
	  s.insert(np);
	}
	if(!excess){
	  ans |= 1<<i;
	  REP(y,H) REP(x,W){
		PII p = db[y][x];
		db[y][x] = xs[i][p.FF][p.SS];
	  }
	}
  }
  cout << ans+1 << endl;

  return 0;
}
### Prompt

Please create a solution in CPP to the following problem:

problem

A dance party with $ N $ people is held at a dance hall. The dance hall is divided into $ H $ vertical and $ W $ horizontal grids, with $ (0,0) $ in the upper left, $ r $ squares from the top, and $ c $ squares from the left. The coordinates of the grid of the eyes are expressed as $ (r, c) $. The initial position of the $ i $ th participant is $ (R_i, C_i) $, and the $ (i, j) $ grid contains $ (r_ {ij}, c_ {ij}) $. ..

Each participant simultaneously moves to the endless music as follows.

* When the coordinates at that time are $ (i, j) $, jump to $ (r_ {ij}, c_ {ij}) $.



Each grid is narrow and will collide if two or more participants move to the same grid at the same time. However, it is assumed that there is no collision in the air. When you heard this, you were worried that two or more participants would collide after the jump. Therefore, I decided to find out if there was a possibility of a collision, and if so, how many jumps the collision would occur after.



output

If a collision occurs, output in one line how many jumps it will occur after. If not, output -1. Also, output a line break at the end.

Example

Input

2 2 2
1 0 0 1
0 0 1 0
0 0
0 1


Output

-1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;

using VI = vector<int>;
using VVI = vector<VI>;
using PII = pair<int, int>;
using LL = long long;
using VL = vector<LL>;
using VVL = vector<VL>;
using PLL = pair<LL, LL>;
using VS = vector<string>;

#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

#define FF first
#define SS second
template<class S, class T>
istream& operator>>(istream& is, pair<S,T>& p){
  return is >> p.FF >> p.SS;
}
template<class S, class T>
ostream& operator<<(ostream& os, const pair<S,T>& p){
  return os << p.FF << " " << p.SS;
}
template<class T>
void maxi(T& x, T y){
  if(x < y) x = y;
}
template<class T>
void mini(T& x, T y){
  if(x > y) x = y;
}


const double EPS = 1e-10;
const double PI  = acos(-1.0);
const LL MOD = 1e9+7;

int H, W, N;
PII xs[18][500][500];

int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  cin >> H >> W >> N;
  REP(y,H) REP(x,W)
	cin >> xs[0][y][x];

  vector<PII> ps(N);
  REP(i,N) cin >> ps[i];

  for(int i=1;i<18;++i){
	REP(y,H) REP(x,W){
	  auto&& par = xs[i-1][y][x];
	  xs[i][y][x] = xs[i-1][par.FF][par.SS];
	}
  }

  bool no = true;
  set<PII> s;
  for(auto&& p: ps){
	PII np = xs[17][p.FF][p.SS];
	if(s.count(np)){
	  no = false;
	}
	s.insert(np);
  }
  if(no){
	cout << -1 << endl;
	return 0;
  }

  int ans = 0;
  vector<vector<PII>> db(H, vector<PII>(W));
  REP(y,H) REP(x,W) db[y][x] = MP(y,x);
  for(int i=17;i>=0;--i){
	bool excess = false;
	set<PII> s;
	for(auto&& p: ps){
	  PII np = db[p.FF][p.SS];
	  np = xs[i][np.FF][np.SS];
	  if(s.count(np)){
		excess = true;
		break;
	  }
	  s.insert(np);
	}
	if(!excess){
	  ans |= 1<<i;
	  REP(y,H) REP(x,W){
		PII p = db[y][x];
		db[y][x] = xs[i][p.FF][p.SS];
	  }
	}
  }
  cout << ans+1 << endl;

  return 0;
}
```