P7028 [NWRRC 2017] Joker

Joker prepares a new card trick with a strong mathematical background. You are asked to help Joker with calculations. There is a row of $n$ cards with non-zero numbers $a_{i}$ written on them. Let's call the sum of all positive numbers $P$ and the sum of all negative numbers $N$ . Every card $i$ has a weight $w_{i} = a_{i}/P$ if $a_{i} > 0$ and $a_{i}/|N|$ otherwise. Let's denote $s_{i} = ( \sum_{j=1}^{j \le i}{w_j})$. Joker needs to know positive $i$ with the largest $s_{i}.$ If there is more than one such $i$ , he is interested in the smallest one. But static tricks are boring, so Joker wants to change numbers on some cards, and after each change he needs to known where is the largest $s_{i}$ is.

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Time limit: 3 s, Memory limit: 512 MB.