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>
using namespace std;
typedef long long ll;
const int N=500025,inf=0x3f3f3f3f;
int read(){
	int f=1,g=0;
	char ch=getchar();
	for (;!isdigit(ch);ch=getchar()) if (ch=='-') f=-1;
	for (;isdigit(ch);ch=getchar()) g=g*10+ch-'0';
	return f*g;
}
int n,a[N],ans,k;
int stk[N],cnt[N],top;
bool add(int x){
	if (x==0) return false;
	if (stk[top]!=x){
		stk[++top]=x;
		cnt[top]=0;
	}
	if ((++cnt[top])==k){
		top--;
		if (!add(x-1)) return false;
	}
	return true;
}
bool check(){
	if (k==1){
		for (int i=1;i<=n;i++)
		if (a[i]<=a[i-1]) return false;
		return true;
	}
	top=0;
	for (int i=1;i<=n;i++){
		if (a[i]<=a[i-1]){
			while (stk[top]>a[i]) top--;
			if (!add(a[i]))
			return false;
		}
	}
	return true;
}
int main(){
//	freopen("balance.in","r",stdin);
//	freopen("balance.out","w",stdout);
	n=read();
	for (int i=1;i<=n;i++) a[i]=read();
	int l=1,r=n;
	while (l<r){
		k=(l+r)>>1;
		if (check()) r=k;
		else l=k+1;
	}
	printf("%d\n",l);
	return 0;
}