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
from collections import deque
N=int(input())
A=[int(i) for i in input().split()]
def f(K):
    L=deque()
    L.append([0,A[0]])
    for i in range(N-1):
        #print(L)
        if A[i]<A[i+1]:
            L.append([0,A[i+1]-A[i]])
            continue
        t=A[i]-A[i+1]
        while t-L[-1][1]>=0:
            t-=L[-1][1]
            L.pop()
            #print(L)
        L[-1][1]-=t
        #if L[-1][1]==0:
            #L.pop()
        if L[-1][0]!=K-1:
            if L[-1][1]==1:
                L[-1][0]+=1
            else:
                L[-1][1]-=1
                L.append([L[-1][0]+1,1])
        else:
            s=0
            while len(L)!=0 and L[-1][0]==K-1:
                s+=L[-1][1]
                L.pop()
            if len(L)==0:
                return False
            elif L[-1][1]==1:
                L[-1][0]+=1
                L.append([0,s])
            elif L[-1][1]!=1:
                L[-1][1]-=1
                L.append([L[-1][0]+1,1])
                L.append([0,s])
    #print(L)
    return True



mi=0
ma=2*10**5+1
while ma-mi>1:
    mid=(ma+mi)//2
    if f(mid):
        ma=mid
    else:
        mi=mid
print(ma)
