Luigi has ** N** balls. The balls look identical. However, there is

**ball that is**

`one`**. The rest share the same weight. Luigi is so cool he has a balance to weigh the balls.**

`heavier` At each ** weighing** he can choose

**of balls and compare them.**

`two disjoint subsets` Luigi wants to compute the ** minimum number of weighings** after which he is 100% sure which ball is the special one.

### Input

The first line of the input contains an integer ** N** denoting the number of balls.

### Output

The only line of output should contain an integer denoting the minimum number of weighings after which he is 100% sure which ball is the heavier one.

### Restrictions

`1 ≤ N ≤ 10`^{18}- Two sets are disjoint if and only if they have no element in common.

### Sample

Input | Output | Explanation |
---|---|---|

2 | 1 | We can compare the two balls and see which one is heavier. |

4 | 2 | We can make 2 groups of 2 balls each and decide which is heavier. Then, we can split that group in 2 groups of 1 ball, compare them and decide which is the heavier among all. |

9 | 2 |

Let's examine the case with 9 balls.

First of all, we can group the 9 balls in the 3 groups, each having 3 balls. Let's call them group1, group2 and group3.

We will weight 2 of them and it will result some cases:

- (group1 == group2) - if the 2 groups we weight are equal then the heavier ball will be in the 3rd group which we have not weighted yet (group3)
- (group1 != group2) - if one of them is heavier then we have found the group which is heavier so either group1 or group2
Now we only have 3 balls left to weight (in each of the 2 cases described above). We apply the same idea again. So, we will weight only 2 balls and see if they are equal then the heavier is the 3rd one. Else one of the 2 balls is the one.

So we have managed to find the heavier ball by making only 2 weighings. Now we can apply the same idea (of splitting the input into 3 groups) to any input. So, the answer will be log3(n-1) which can be calculated in O(1) or in O(log3(n))