A11716 | Equator

Polycarp has created his own training plan to prepare for the programming contests. He will train for $n$ days, all days are numbered from $1$ to $n$ , beginning from the first.

On the $i$ -th day Polycarp will necessarily solve $a_i$ problems. One evening Polycarp plans to celebrate the equator. He will celebrate it on the first evening of such a day that from the beginning of the training and to this day inclusive he will solve half or more of all the problems.

Determine the index of day when Polycarp will celebrate the equator.

The first line contains a single integer $n$ ( $1 \le n \le 200\,000$ ) — the number of days to prepare for the programming contests.

The second line contains a sequence $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 10\,000$ ), where $a_i$ equals to the number of problems, which Polycarp will solve on the $i$ -th day.

Print the index of the day when Polycarp will celebrate the equator.