A. Mahmoud and Ehab and the even-odd game

Codeforces

IDCF959A

Time1000ms

Memory256MB

Difficulty—

gamesmath

English · Original

Chinese · Translation

Formal · Original

Mahmoud and Ehab play a game called the even-odd game. Ehab chooses his favorite integer _n_ and then they take turns, starting from Mahmoud. In each player's turn, he has to choose an integer _a_ and subtract it from _n_ such that: * 1 ≤ _a_ ≤ _n_. * If it's Mahmoud's turn, _a_ has to be even, but if it's Ehab's turn, _a_ has to be odd. If the current player can't choose any number satisfying the conditions, he loses. Can you determine the winner if they both play optimally? ## Input The only line contains an integer _n_ (1 ≤ _n_ ≤ 109), the number at the beginning of the game. ## Output Output "_Mahmoud_" (without quotes) if Mahmoud wins and "_Ehab_" (without quotes) otherwise. [samples] ## Note In the first sample, Mahmoud can't choose any integer _a_ initially because there is no positive even integer less than or equal to 1 so Ehab wins. In the second sample, Mahmoud has to choose _a_ = 2 and subtract it from _n_. It's Ehab's turn and _n_ = 0. There is no positive odd integer less than or equal to 0 so Mahmoud wins.

Mahmoud 和 Ehab 玩一个叫做偶奇游戏的游戏。Ehab 选择他最喜欢的整数 $n$，然后他们轮流进行，从 Mahmoud 开始。在每个玩家的回合中，他必须选择一个整数 $a$ 并从 $n$ 中减去它，使得：如果当前玩家无法选择任何满足条件的数字，他就输了。如果双方都采取最优策略，你能确定获胜者吗？唯一的一行包含一个整数 $n$ $(1 ≤ n ≤ 10^9)$，即游戏开始时的数字。如果 Mahmoud 获胜，请输出 "_Mahmoud_"（不含引号），否则输出 "_Ehab_"（不含引号）。在第一个测试用例中，Mahmoud 最初无法选择任何整数 $a$，因为不存在小于或等于 $1$ 的正偶整数，因此 Ehab 获胜。在第二个测试用例中，Mahmoud 必须选择 $a = 2$ 并从 $n$ 中减去它。轮到 Ehab 时，$n = 0$。不存在小于或等于 $0$ 的正奇整数，因此 Mahmoud 获胜。 ## Input 唯一的一行包含一个整数 $n$ $(1 ≤ n ≤ 10^9)$，即游戏开始时的数字。 ## Output 如果 Mahmoud 获胜，请输出 "_Mahmoud_"（不含引号），否则输出 "_Ehab_"（不含引号）。 [samples] ## Note 在第一个测试用例中，Mahmoud 最初无法选择任何整数 $a$，因为不存在小于或等于 $1$ 的正偶整数，因此 Ehab 获胜。在第二个测试用例中，Mahmoud 必须选择 $a = 2$ 并从 $n$ 中减去它。轮到 Ehab 时，$n = 0$。不存在小于或等于 $0$ 的正奇整数，因此 Mahmoud 获胜。

**Definitions** Let $ n \in \mathbb{Z}^+ $ be the initial integer, with $ 1 \leq n \leq 10^9 $. Players alternate turns, starting with Mahmoud. On a player’s turn, they must choose a positive integer $ a $ such that: - If it is Mahmoud’s turn, $ a $ must be even and $ a \leq n $. - If it is Ehab’s turn, $ a $ must be odd and $ a \leq n $. The player unable to make a valid move loses. **Constraints** $ 1 \leq n \leq 10^9 $ **Objective** Determine the winner under optimal play: - Output "Mahmoud" if the first player (Mahmoud) has a winning strategy. - Output "Ehab" otherwise.

Samples

Input #1

Output #1

Ehab

Input #2

Output #2

Mahmoud

API Response (JSON)

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