A. Generous Eater

Codeforces

IDCF10219A

Time2000ms

Memory256MB

Difficulty—

English · Original

Formal · Original

You have n candies. You want to give as much to your friends as possible, but you have a problem; every time you give two friends a candy each, you can't help but eat one yourself (if you have one left). You tried to resist after giving the first one, but after giving the second, it was unbearable. What is the maximum number of friends you can give candies to? The first line of input contains n (1 ≤ n ≤ 109), the number of candies you have. Output a single line with the maximum number of friends you can give candies to. ## Input The first line of input contains n (1 ≤ n ≤ 109), the number of candies you have. ## Output Output a single line with the maximum number of friends you can give candies to. [samples]

**Definitions** Let $ n \in \mathbb{Z} $ be the number of candies, with $ 1 \leq n \leq 10^9 $. **Constraints** For every two candies given to two friends, one candy is consumed by the giver (i.e., a cost of 1 candy per 2 friends). **Objective** Maximize the number of friends $ f \in \mathbb{Z}_{\geq 0} $ such that: $$ f \leq 2 \left\lfloor \frac{n}{3} \right\rfloor + \min\left(n \bmod 3, 1\right) $$ Equivalently: $$ f = \left\lfloor \frac{2n}{3} \right\rfloor $$

API Response (JSON)

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