There are $n$ apples on Little Y's table, arranged in a row from left to right, numbered from $1$ to $n$.
Little Bao is a good friend of Little Y, and every day she takes away some apples.
Each day, when taking apples, Little Bao starts from the first apple on the left and takes one apple every three apples (i.e., she takes the 1st, 4th, 7th, ... apples).
Afterward, Little Bao rearranges the remaining apples in a row in their original order.
Little Bao wants to know how many days it will take to finish all the apples, and on which day the apple numbered $n$ is taken.
Input
The input consists of a single positive integer $n$, representing the total number of apples.
Output
Output a single line containing two positive integers separated by a space, representing the number of days it takes for Little Bao to take all the apples and the day on which the apple numbered $n$ is taken, respectively.
Constraints
For all test data, $1 \le n \le 10^9$.
| Test Cases | $n \le$ | Special Property |
|---|---|---|
| $1 \sim 2$ | $10$ | None |
| $3 \sim 5$ | $10^3$ | None |
| $6 \sim 7$ | $10^6$ | Yes |
| $8 \sim 9$ | $10^6$ | None |
| $10$ | $10^9$ | None |
Special property: Little Bao takes the apple numbered $n$ on the first day.
Examples
Input 1
8
Output 1
5 5
Note
There are a total of $8$ apples on Little Bao's table. On the first day, Little Bao takes apples numbered $1, 4, 7$. On the second day, Little Bao takes apples numbered $2, 6$. On the third day, Little Bao takes apple numbered $3$. On the fourth day, Little Bao takes apple numbered $5$. On the fifth day, Little Bao takes apple numbered $8$.