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 <map>

using namespace std;

const int MAXN=200111;

int N, K;
int A[MAXN];

struct Node{
	int p, v;
	Node(){}
	Node(int _p, int _v){p=_p;v=_v;}
};

Node St[MAXN];
int Top;

bool Push(int p){
	if(!p)	return false;
	while(Top>0 && St[Top].p>p)	--Top;
	if(St[Top].p==p)	++St[Top].v;
	else	St[++Top]=Node(p, 1);
	if(St[Top].v==K){
		p=St[Top].p;
		--Top;
		return Push(p-1);
	}
	return true;
}

bool Test(int k){
	
	K=k;
	Top=0;
	
	bool ret=true;
	
	for(int i=2;i<=N && ret;++i){
		if(A[i]<=A[i-1]){
			ret&=Push(A[i]);
		}
	}
	
	return ret;
}

int main(){
	ios_base::sync_with_stdio(false);
	
	cin >> N;
	
	for(int i=1;i<=N;++i)	cin >> A[i];
	
	int Left=1, Right=N, Mid;
	while(Left<Right){
		Mid=(Left+Right)>>1;
		if(Test(Mid))	Right=Mid;
		else	Left=Mid+1;
	}
	Mid=(Left+Right)>>1;
	
	cout << Mid << endl;
	
	return 0;
}