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>
using namespace std;
typedef long long ll;
const int maxn=2e5+10;
int n,aaa[maxn],pos[maxn],num[maxn];
int top,ans;
bool check(int ans)
{
    top=0;
    for(int i=2;i<=n;i++)
    if(aaa[i]<=aaa[i-1])
    {
        int x=aaa[i];
        while(top&&pos[top]>x) top--;
        while(top&&pos[top]==x&&num[top]==ans) top--,x--;
        if(x==0) return 0;
        else if(pos[top]<x)
        {
            pos[++top]=x;
            num[top]=2;
            if(ans==1)
                return 0;
        }
        else num[top]++;
    }
    return 1;
}
int main(int argc, char** argv)
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&aaa[i]);
    int l=1,r=n,ans;
    while(l<=r)
    {
        int mid=(l+r)>>1;
        if(check(mid))
            r=mid-1,ans=mid;
        else
            l=mid+1;
    }
    printf("%d\n",ans);
    return 0;
}
