Dutch Democracy

The process of forming the Dutch government has taken more than half a year for three elections in a row. Perhaps we can streamline the initial stages of coalition building?

The first step after the election results is to find a group of parties (called a coalition) with enough seats to have a strict majority. Your task is to count the number of candidate coalitions that satisfy specific conditions. A coalition is considered a candidate coalition if it meets these two criteria:

Strict Majority: The total number of seats held by the coalition must be strictly more than half of the total seats across all parties.

No Superfluous Parties: The coalition must be minimal in the sense that removing any one party from the coalition would cause it to lose its strict majority.

Figure D.1: Illustration of Sample Input 2.

The input consists of:

• One line with an integer $n$ ($1 \le n \le 60$), the number of parties.
• One line with $n$ integers $p$ ($1 \le p \le 10\,000$), the number of seats each party has.

Output the total number of candidate coalitions that satisfy the criteria above.