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 rep(i,x,y) for (int i=(x);i<=(y);i++)
using namespace std;
const int N=2e5+5;
int n,a[N];
bool check(int m){
	map<int,int> s;
	rep (i,2,n){
		if (a[i-1]<a[i]) continue;
		if (m==1) return 0;
		int x=a[i];
		s.erase(s.upper_bound(x),s.end());
		while (s[x]==m-1){
			x--;
			if (x==0) return 0;
		}
		s.erase(s.upper_bound(x),s.end());
		s[x]++;
	}
	return 1;
}
int main(){	
	scanf("%d",&n);
	rep (i,1,n) scanf("%d",&a[i]);
	int l=1,r=n,mid;
	while (l<=r){
		mid=l+r>>1;
		if (check(mid)) r=mid-1; else l=mid+1;
	}
	printf("%d\n",r+1);
	return 0;
}