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<iomanip>
#include<cstring>
#include<cmath>
#include<cstdio>
#include<queue>
#include<algorithm>
using namespace std;
int n;
int a[200005],l,r,tail;
struct que
{
	int x,v;
}sta[200005];
void insert(int x,int v)
{
	while(sta[tail].x>x) tail--;
	if(sta[tail].x==x) sta[tail].v++;
	else sta[++tail]=(que){x,1};
	if(tail>1&&sta[tail].v==v) tail--,insert(x-1,v);
}
bool check(int v)
{
	tail=0;
	sta[++tail]=(que){0,0};
	for(int i=2;i<=n;i++) if(a[i]<=a[i-1]) insert(a[i],v);
	return !sta[1].v;
}
int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;i++) scanf("%d",&a[i]);
	bool flag=1;
	for(int i=2;i<=n;i++) if(a[i]<=a[i-1]) flag=0;
	if(flag)
	{
		puts("1");
		return 0;
	}
	l=2,r=n;
	while(l<r)
	{
		int mid=(l+r)>>1;
		if(check(mid)) r=mid;
		else l=mid+1;
	}
	printf("%d",l);
}