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<cstdio>
#define RI register int
#define CI const int&
using namespace std;
const int N=200005;
int n,a[N],stk[N],c[N],top,ans;
inline bool check(CI lim)
{
	if (lim==1)
	{
		for (RI i=2;i<=n;++i) if (a[i]<=a[i-1]) return 0; return 1; 
	}
	top=0; for (RI i=2;i<=n;++i) if (a[i]<=a[i-1])
	{
		int x=a[i]; while (top&&stk[top]>x) --top;
		while (top&&stk[top]==x&&c[top]==lim) --top,--x;
		if (!x) return 0; if (stk[top]==x) ++c[top]; else stk[++top]=x,c[top]=2;
	}
	return 1;
}
int main()
{
	RI i; for (scanf("%d",&n),i=1;i<=n;++i) scanf("%d",&a[i]);
	int l=1,r=n,mid; while (l<=r)
	if (check(mid=l+r>>1)) ans=mid,r=mid-1; else l=mid+1;
	return printf("%d",ans),0;
}