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
N=int(input())
A=list(map(int,input().split()))
def judge(X):
  Y=[[A[0],1]]
  Z=0
  for i in range(N-1):
    if A[i]<A[i+1]:
      Y.append([A[i+1]-A[i],1])
    else:
      Z=A[i]-A[i+1]
      for j in range(len(Y)):
        if Y[-1][0]<=Z:
          Z-=Y[-1][0]
          del Y[-1]
        else:
          Y[-1][0]-=Z
          break
      Z=0
      for j in range(len(Y)-1,-2,-1):
        if j==-1:
          return False
        if Y[j][1]==X or Y[j][0]==0:
          Z+=Y[j][0]
          del Y[j]
        else:
          if Y[j][0]==1:
            Y.append([1,Y[j][1]+1])
            del Y[j]
          else:
            Y[j][0]-=1
            Y.append([1,Y[j][1]+1])
          if Z:
            Y.append([Z,1])
          break
  return True

L,R,M=1,10**9,0
while R>L:
  M=(L+R)//2
  if judge(M):
    R=M
  else:
    L=max(L+1,M)
print(L)