Mafia in Potokolandia

In Potokolandia, a new online version of the game "Mafia" has been developed.

Kozak Vus, the chief programmer of Potokolandia, is responsible for testing this game.

A key feature of "Mafia" is its message chats. Kozak Vus considers the game successfully tested if the chats contain at least $n$ words in total.

Since programmers do not test chats, Kozak needs to hire testers under the following conditions: each tester will write a greeting message with $a$ words in the game's general chat and also send a greeting message with $b$ words to each other tester in a personal chat. Testers will not write any other messages beyond these.

For example, if there are $3$ testers, each will write "Hello everyone!" ($2$ words) in the general chat and "Hi!" ($1$ word) to each other tester in a personal chat. This results in $2\cdot 3=6$ words in the general chat (each tester writes $2$ words), and $2$ words in each personal chat (one from each tester). With $3$ personal chats in total (between the first and second, first and third, and second and third testers), $3\cdot 2=6$ words will be written in personal chats. Thus, a total of $6+6=12$ words will be written in all chats.

During testing, only testers will write messages in the chats.

Kozak Vus wants to minimize the cost of hiring testers, so he aims to hire the fewest number possible. Help him determine the minimum number of testers required to ensure at least $n$ words are written in the chats.

Input

The first line contains three integers $n$, $a$, and $b$ ($1\le n\le 10^{12}$, $0\le a,b\le 10^6$, $0<a+b$) — the minimum number of words that must be written, the number of words each tester writes in the general chat, and the number of words each tester writes to each other in a personal chat.

Output

Output a single integer — the minimum number of testers needed to ensure at least $n$ words are written in the chats.

Examples

Note

In the first example, if $3$ testers are hired, $3$ words will be written in the general chat, and $18$ words will be written in personal chats.

In the second example, if $2$ testers are hired, $16$ words will be written in the general chat, and $4$ words will be written in personal chats.

Scoring

Each test, except for the examples, is worth $5$ points.