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<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
inline int read(){
	int x=0,f=1;char ch;
	do{ch=getchar();if(ch=='-')f=-1;}while(ch<'0'||ch>'9');
	do{x=x*10+ch-'0';ch=getchar();}while(ch>='0'&&ch<='9');
	return x*f;
}
const int N=400010,INF=0x3f3f3f3f;
int a[N],n;
struct DATA{
	int x,y;
}s[N];
int ls,mid;
inline void insert(int x){
	if (s[ls].x>x){
		while (s[ls].x>x) --ls;
		if (s[ls].x<x) s[++ls]=(DATA){x,1};
	}
	if (s[ls].x==x){
		++s[ls].y;
		if (s[ls].y>mid) insert(x-1),s[++ls]=(DATA){x,1};
	}
	else s[++ls]=(DATA){x,1};
}
inline bool judge(){
	ls=0;
	s[++ls]=(DATA){0,0};
	for (int i=1;i<=n;++i){
		if (mid==1&&a[i]<=a[i-1]) return 0;
		insert(a[i]);
		if (s[1].y) return 0;
	}
	return 1;
}
int main(){
	n=read();
	for (int i=1;i<=n;++i) a[i]=read();
	int l=1,r=n;
	while (l<r){
		mid=(l+r)>>1;
		if (judge()) r=mid;
		else l=mid+1;
	}
	printf("%d\n",l);
	return 0;
}