Residents of Partoburg often violate traffic rules, get into accidents involving scooters, and steal other people's scooters. In order to control scooter-related incidents, the sheriff of Partoburg has introduced a scooter registration system.

On the first day of each month the sheriff chooses a natural number $$$n$$$ and prints all possible scooter numbers in the format $$$[a_{1}+a_{2}+ \ldots +a_{k}]$$$, where $$$a_1+a_2+\ldots+a_k = n$$$, and natural numbers $$$a_{i}$$$ are ordered non-decreasingly: $$$a_1 \le a_2 \le \ldots \le a_{k}$$$. Each number is unique: there cannot be two scooters with the same number. The numbers are assigned to scooter owners. If an owner does not have a number in a given month, he cannot use the scooter during that month.

The sheriff himself also moves around on a scooter. To easily identify his scooter, it has a special number format. The sheriff's scooter number is a single number calculated as follows. For all scooter numbers in the current month $$$[a_{1}+a_{2}+ \ldots +a_{k}]$$$, the value $$$\mathrm{mex}{a_{1},a_{2}, \ldots, a_{k}}$$$ is calculated — the minimum natural number absent in the number. These values are summed. The number of the sheriffs scooter is a remainder of the division of the resulting sum by $$$10^9+7$$$.

The sheriff wants to automate the scooter number assignment system and started with his own scooter. This month he chose the number $$$n$$$. Help determine what number his scooter will receive.