One day n cells of some array decided to play the following game. Initially each cell contains a number which is equal to it's ordinal number (starting from 1). Also each cell determined it's favourite number. On it's move i-th cell can exchange it's value with the value of some other j-th cell, if |i - j| = d_i, where d_i is a favourite number of i-th cell. Cells make moves in any order, the number of moves is unlimited.

The favourite number of each cell will be given to you. You will also be given a permutation of numbers from 1 to n. You are to determine whether the game could move to this state.

The first line contains positive integer n (1 ≤ n ≤ 100) — the number of cells in the array. The second line contains n distinct integers from 1 to n — permutation. The last line contains n integers from 1 to n — favourite numbers of the cells.

If the given state is reachable in the described game, output YES, otherwise NO.

5
5 4 3 2 1
1 1 1 1 1

YES

7
4 3 5 1 2 7 6
4 6 6 1 6 6 1

NO

7
4 2 5 1 3 7 6
4 6 6 1 6 6 1

YES

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>

int fa[105],p[105],love[105];

int find(int x)
{
	if(fa[x]!=x)
		fa[x] = find(fa[x]);
	return fa[x];
}

void build(int x,int y)
{
	int a=find(x);
	int b=find(y);
	fa[a] = b;
}

int main()
{
	int n,q;
	long long ans;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
		fa[i] = i;
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&q);
		p[q]=i;
	}
	for(int i=1;i<=n;i++)
	{
		scanf("%d",&love[i]);
	}
	for(int i=1;i<=n;i++)
	{
		if(i-love[i]>=1)
		build(i,i-love[i]);
		if(i+love[i]<=n)
		build(i,i+love[i]);
	}
	int f=1;
    for(int i=1;i<=n;i++)
    {
		if(find(p[i])!=find(i))
		{
			f=0;
			break;
		}
    }
	if(f==1)
	{
		printf("YES\n");
	}
	else
	{
		printf("NO\n");
	}
	return 0;
}