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>

inline int read(){
	char c=getchar(); int x=0,ft=1;
	for(;c<'0'||c>'9';c=getchar()) if(c=='-') ft=-1;
	for(;c>='0'&&c<='9';c=getchar()) x=x*10+c-'0';
	return x*ft;
}

const int N=2e5+5;

int n,a[N],s[N],c[N],top;

void insert(int x){
	if(s[top]<x) s[++top]=x,c[top]=1; else ++c[top];
}

bool check(int k){
	top=0;
	for(int i=2;i<=n;++i) if(a[i-1]>=a[i]){
		while(top&&s[top]>a[i]) --top; insert(a[i]);
		while(top&&c[top]==k){
			int pos=s[top--]; if(pos==1) return 0; insert(pos-1);
		}
	}
	return 1;
}

int main(){
	n=read();
	for(int i=1;i<=n;++i) a[i]=read();
	int l=1,r=n,mid;
	while(l<r){
		mid=(l+r)>>1;
		if(check(mid)) r=mid; else l=mid+1;
	}
	printf("%d\n",l);
	return 0;
}