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<bits/stdc++.h>
#define reg register
typedef long long ll;
using namespace std;
const int MN=2e5+5;
int n,len[MN],stk[MN],val[MN],top;
inline void insert(int pos,int x){
	while(stk[top]>pos)top--;
	if(stk[top]==pos)val[top]++;
	else stk[++top]=pos,val[top]=1;
	if(top&&val[top]==x)top--,insert(pos-1,x);
}
bool check(int x){
	stk[top=0]=val[0]=0;
	for(reg int i=2;i<=n;i++)
		if(len[i-1]>=len[i])insert(len[i],x);
	return !val[0];
}
int main(){
	scanf("%d",&n);
	for(reg int i=1;i<=n;i++)scanf("%d",len+i);
	reg int flg=1;
	for(reg int i=2;flg&&i<=n;i++)
		if(len[i]<=len[i-1])flg=0;
	if(flg)return 0*puts("1");
	reg int l=2,r=n,ans=n,mid;
	while(l<=r){
		mid=(l+r>>1);
		if(check(mid))r=mid-1,ans=mid;
		else l=mid+1;
	}
	printf("%d\n",ans);
	return 0;
}