CF1043A Elections

Awruk is taking part in elections in his school. It is the final round. He has only one opponent — Elodreip. The are $ n $ students in the school. Each student has exactly $ k $ votes and is obligated to use all of them. So Awruk knows that if a person gives $ a_i $ votes for Elodreip, than he will get exactly $ k - a_i $ votes from this person. Of course $ 0 \le k - a_i $ holds. Awruk knows that if he loses his life is over. He has been speaking a lot with his friends and now he knows $ a_1, a_2, \dots, a_n $ — how many votes for Elodreip each student wants to give. Now he wants to change the number $ k $ to win the elections. Of course he knows that bigger $ k $ means bigger chance that somebody may notice that he has changed something and then he will be disqualified. So, Awruk knows $ a_1, a_2, \dots, a_n $ — how many votes each student will give to his opponent. Help him select the smallest winning number $ k $ . In order to win, Awruk needs to get strictly more votes than Elodreip.

The first line contains integer $ n $ ( $ 1 \le n \le 100 $ ) — the number of students in the school. The second line contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 1 \leq a_i \leq 100 $ ) — the number of votes each student gives to Elodreip.

Output the smallest integer $ k $ ( $ k \ge \max a_i $ ) which gives Awruk the victory. In order to win, Awruk needs to get strictly more votes than Elodreip.

In the first example, Elodreip gets $ 1 + 1 + 1 + 5 + 1 = 9 $ votes. The smallest possible $ k $ is $ 5 $ (it surely can't be less due to the fourth person), and it leads to $ 4 + 4 + 4 + 0 + 4 = 16 $ votes for Awruk, which is enough to win. In the second example, Elodreip gets $ 11 $ votes. If $ k = 4 $ , Awruk gets $ 9 $ votes and loses to Elodreip.