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>
const int N=2e5+6;
int n,A[N];
int a[N],b[N],top;
bool check(int c){
    top=0;
    for(int i=2;i<=n;++i)
    if(A[i]<=A[i-1]){
        int pos=A[i];
        while(top&&a[top]>pos)--top;
        if(!top||a[top]!=pos)a[++top]=pos,b[top]=1;else{
            while(top&&a[top]==pos&&b[top]==c-1)--top,--pos;
            if(!pos)return 0;
            if(top&&a[top]==pos)++b[top];else a[++top]=pos,b[top]=1;
        }
    }
    return 1;
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;++i)scanf("%d",A+i);
    bool ok=1;
    for(int i=1;i<=n;++i)if(A[i]<=A[i-1])ok=0;
    if(ok){puts("1");return 0;}
    int l=2,r=1e9,ans=1e9;
    while(l<=r){
        const int mid=l+r>>1;
        if(check(mid))r=(ans=mid)-1;else l=mid+1;
    }
    printf("%d\n",ans);
    return 0;
}