There are N strings arranged in a row. It is known that, for any two adjacent strings, the string to the left is lexicographically smaller than the string to the right. That is, S_1<S_2<...<S_N holds lexicographically, where S_i is the i-th string from the left.

At least how many different characters are contained in S_1,S_2,...,S_N, if the length of S_i is known to be A_i?

Constraints

* 1 \leq N \leq 2\times 10^5
* 1 \leq A_i \leq 10^9
* A_i is an integer.

Input

Input is given from Standard Input in the following format:


N
A_1 A_2 ... A_N


Output

Print the minimum possible number of different characters contained in the strings.

Examples

Input

3
3 2 1


Output

2


Input

5
2 3 2 1 2


Output

2
#include<cstdio>
const int N=2e5+3;
struct segment{int l,r,f;}b[N];
int n,a[N],t;
inline bool Check(int m){
	t=0;
	for(int i=2;i<=n;i++)if(a[i]<=a[i-1]){
	  if(!m)return 0;
	  for(;t&&b[t].l>a[i];--t);
	  if(t&&b[t].r>a[i])b[t].r=a[i];
	  if(t&&b[t].r==a[i]){
		if(!b[t].l)return 0;
	  }
	  else{
		b[++t]=(segment){a[i],a[i],0};
	  }
	  b[t]=(segment){b[t].l,b[t].l,b[t].f+1};
	  if(b[t].f==m){
		b[t].l--,b[t].f=0;
		if(t>1&&b[t-1].r==b[t].l)
		  b[t-1].r=a[i],--t;
	  }
	}return 1;
}
int main(){
	int l,r,m;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)scanf("%d",a+i);
	for(l=0,r=n;l<r;)m=l+r>>1,Check(m)?r=m:l=m+1;
	printf("%d\n",l+1);
	return 0;
}