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>
no_of_cubes = int(input())
data = [0]
layer =0
sum = 0
while(data[layer] <= no_of_cubes):
    layer+=1
    if layer==1:
        sum += data[layer - 1] + layer
        if sum > no_of_cubes:
            break
        else :
            data.append(layer)
    elif layer==2:
        sum += data[layer - 1] + layer
        if sum > no_of_cubes:
            break
        else :
            data.append(data[layer-1]+layer)


    elif layer > 2 :
        if data[layer-1]+layer < no_of_cubes:
            sum += data[layer - 1] + layer
            if sum > no_of_cubes:
                break
            else:
                data.append(data[layer-1]+layer)

        else:
            break

print(len(data)-1)




