Vanya got n cubes. He decided to build a pyramid from them. Vanya wants to build the pyramid as follows: the top level of the pyramid must consist of 1 cube, the second level must consist of 1 + 2 = 3 cubes, the third level must have 1 + 2 + 3 = 6 cubes, and so on. Thus, the i-th level of the pyramid must have 1 + 2 + ... + (i - 1) + i cubes.

Vanya wants to know what is the maximum height of the pyramid that he can make using the given cubes.

Input

The first line contains integer n (1 ≤ n ≤ 104) — the number of cubes given to Vanya.

Output

Print the maximum possible height of the pyramid in the single line.

Examples

Input

1


Output

1


Input

25


Output

4

Note

Illustration to the second sample: 

<image>
n = int(input())

arr = []

s,i,prev = 0,1,0

while s+prev <= 10**4:
    
    s += i
    
    arr.append(s+prev)
    
    i += 1
    
    prev = arr[-1]
    
arr.append(s+prev)

lb,ub,flag = 0,len(arr)-1,0

while lb <= ub:
    
    mid = (lb + ub)//2
    
    if arr[mid] == n:
        
        flag = 1
        
        break
    
    elif arr[mid] > n:
        
        ub = mid - 1
        
    else:
        
        lb = mid + 1
    
if flag == 1:
    
    print(mid+1)
    
else:
    
    print(lb)