p03202 AtCoder Grand Contest 029 - Lexicographic constraints
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
```python
N=int(input())
A=[int(i) for i in input().split()]
def Check(K):
  stack=[]
  n=A[0]
  for i in range(1,N):
    if A[i-1]<A[i]:
      n=A[i]
    else:
      if K==1:
        return False
      n=A[i]
      while True:
        l=0
        if stack:
          l=stack[-1][0]
        if l>n:
          stack.pop()
        else:
          break       
      k=n
      while k>=1:
        if not stack:
          stack.append([k,1])
          break
        if stack[-1][0]==k:
          if stack[-1][1]==K-1:
            if k!=1:
              stack.pop()
              k-=1
            else:
              return False
          else:
            stack[-1][1]+=1
            break
        else:
          stack.append([k,1])
          break
  return True
l,r=1,N
while l<r:
  m=(l+r)//2
  if Check(m):
    r=m
  else:
    l=m+1
print(l)
          
          
          
      
```