USACO 2020 December

Daisy Chains

Every day, as part of her walk around the farm, Bessie the cow visits her favorite pasture, which has n flowers (all colorful daisies) labeled 1..n lined up in a row. Flower i has pi petals.

As a budding photographer, Bessie decides to take several photos of these flowers. In particular, for every pair of flowers (i, j) satisfying 1ijn, Bessie takes a photo of all flowers from flower i to flower j (including i and j).

Bessie later looks at these photos and notices that some of these photos have an "average flower" - a flower that has p petals, where p is the exact average number of petals among all flowers in the photo.

How many of Bessie's photos have an average flower?


The first line contains n (1n100). The second line contains n integers p1..pn (1 ≤ pi ≤ 1000).


Please print out the number of photos that have an average flower.


Every picture containing just a single flower contributes to the count (there are four of these in the example). Also, the (i, j) ranges (1, 2) and (2, 4) in this example correspond to pictures that have an average flower.

Time limit 1 second
Memory limit 128 MiB
Input example #1
1 1 2 3
Output example #1
Source 2020 USACO December, Bronze