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,s,t) for(int i=s;i<=(t);++i) 
#define dec(i,s,t) for(int i=s;i>=(t);--i)
#define mp(a,b) make_pair(a,b) 
using namespace std;
const int N=3e5+50; 
int n,a[N]; 

bool chk(int x){
	if(x==1){rep(i,2,n)if(a[i]<=a[i-1])return false; return true; }
	set<pair<int,int>> s; 
	rep(j,2,n){
		if(a[j]<=a[j-1]){
			while(!s.empty()&&(s.rbegin()->first>=a[j]))s.erase(*s.rbegin()); 
			dec(i,a[j]-1,0){
				if(s.empty()||s.rbegin()->first!=i){
					s.insert(mp(i,1));
					break;
				}
				if(s.rbegin()->second+1<x){
					auto t=*s.rbegin(); s.erase(*s.rbegin()); ++t.second; s.insert(t); 
					break;
				}else{
					s.erase(*s.rbegin()); 
				}
			}
			if(s.empty())return false;
		}}
	return true;
}

int main() {
	scanf("%d", &n); 
	rep(i,1,n) scanf("%d",a+i); 
	int l=0,r=n; 
	while(r-l>1){
		int mid=(l+r)>>1;
		if(chk(mid))r=mid;
		else l=mid;
	}
	printf("%d\n",r); 
	return 0;
}