#include<bits/stdc++.h>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


struct LOC{
	void set(int arg_to_row,int arg_to_col){
		to_row = arg_to_row;
		to_col = arg_to_col;
	}
	int to_row,to_col;
};

struct Info{
	int row,col;
};

int H,W,N;
int limit = 18;
int POW[19],work[501][501];
LOC table[19][501][501];
Info first_loc[250005],calc_loc[250005];

bool check(int num){

	for(int row = 0; row < H; row++){
		for(int col = 0; col < W; col++)work[row][col] = 0;
	}

	for(int i = 0; i < N; i++){
		calc_loc[i] = first_loc[i];
	}

	int now_row,now_col;

	for(int i = limit; i >= 0; i--){
		if(num < POW[i])continue;
		num -= POW[i];

		for(int k = 0; k < N; k++){
			now_row = calc_loc[k].row;
			now_col = calc_loc[k].col;
			calc_loc[k].row = table[i][now_row][now_col].to_row;
			calc_loc[k].col = table[i][now_row][now_col].to_col;
		}
	}

	for(int i = 0; i < N; i++){
		work[calc_loc[i].row][calc_loc[i].col]++;
		if(work[calc_loc[i].row][calc_loc[i].col] == 2){
			return true;
		}
	}

	return false;
}


int main(){

	for(int i = 0; i <= limit; i++)POW[i] = pow(2,i);

	scanf("%d %d %d",&H,&W,&N);

	int to_row,to_col;

	for(int row = 0; row < H; row++){
		for(int col = 0; col < W; col++){
			scanf("%d %d",&to_row,&to_col);
			table[0][row][col].set(to_row,to_col);
		}
	}

	for(int i = 0; i < N; i++){
		scanf("%d %d",&first_loc[i].row,&first_loc[i].col);
	}

	for(int i = 1; i <= limit; i++){
		for(int row = 0; row < H; row++){
			for(int col = 0; col < W; col++){

				to_row = table[i-1][row][col].to_row;
				to_col = table[i-1][row][col].to_col;

				table[i][row][col].to_row = table[i-1][to_row][to_col].to_row;
				table[i][row][col].to_col = table[i-1][to_row][to_col].to_col;
			}
		}
	}

	int left = 1,right = H*W,m = (left+right)/2;
	int ans = BIG_NUM;

	while(left <= right){
		if(check(m)){
			ans = m;
			right = m-1;
		}else{
			left = m+1;
		}
		m = (left+right)/2;
	}

	if(ans == BIG_NUM){
		printf("-1\n");
	}else{
		printf("%d\n",ans);
	}

	return 0;
}


### Prompt

Develop a solution in CPP to the problem described below:

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>
typedef long long int ll;
typedef unsigned long long int ull;
#define BIG_NUM 2000000000
#define MOD 1000000007
#define EPS 0.000000001
using namespace std;


struct LOC{
	void set(int arg_to_row,int arg_to_col){
		to_row = arg_to_row;
		to_col = arg_to_col;
	}
	int to_row,to_col;
};

struct Info{
	int row,col;
};

int H,W,N;
int limit = 18;
int POW[19],work[501][501];
LOC table[19][501][501];
Info first_loc[250005],calc_loc[250005];

bool check(int num){

	for(int row = 0; row < H; row++){
		for(int col = 0; col < W; col++)work[row][col] = 0;
	}

	for(int i = 0; i < N; i++){
		calc_loc[i] = first_loc[i];
	}

	int now_row,now_col;

	for(int i = limit; i >= 0; i--){
		if(num < POW[i])continue;
		num -= POW[i];

		for(int k = 0; k < N; k++){
			now_row = calc_loc[k].row;
			now_col = calc_loc[k].col;
			calc_loc[k].row = table[i][now_row][now_col].to_row;
			calc_loc[k].col = table[i][now_row][now_col].to_col;
		}
	}

	for(int i = 0; i < N; i++){
		work[calc_loc[i].row][calc_loc[i].col]++;
		if(work[calc_loc[i].row][calc_loc[i].col] == 2){
			return true;
		}
	}

	return false;
}


int main(){

	for(int i = 0; i <= limit; i++)POW[i] = pow(2,i);

	scanf("%d %d %d",&H,&W,&N);

	int to_row,to_col;

	for(int row = 0; row < H; row++){
		for(int col = 0; col < W; col++){
			scanf("%d %d",&to_row,&to_col);
			table[0][row][col].set(to_row,to_col);
		}
	}

	for(int i = 0; i < N; i++){
		scanf("%d %d",&first_loc[i].row,&first_loc[i].col);
	}

	for(int i = 1; i <= limit; i++){
		for(int row = 0; row < H; row++){
			for(int col = 0; col < W; col++){

				to_row = table[i-1][row][col].to_row;
				to_col = table[i-1][row][col].to_col;

				table[i][row][col].to_row = table[i-1][to_row][to_col].to_row;
				table[i][row][col].to_col = table[i-1][to_row][to_col].to_col;
			}
		}
	}

	int left = 1,right = H*W,m = (left+right)/2;
	int ans = BIG_NUM;

	while(left <= right){
		if(check(m)){
			ans = m;
			right = m-1;
		}else{
			left = m+1;
		}
		m = (left+right)/2;
	}

	if(ans == BIG_NUM){
		printf("-1\n");
	}else{
		printf("%d\n",ans);
	}

	return 0;
}


```