F. Fruit Sequencestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputZookeeper is buying a carton of fruit to feed his pet wabbit. The fruits are a sequence of apples and oranges, which is represented by a binary string s_1s_2\ldots s_n of length n. 1 represents an apple and 0 represents an orange.Since wabbit is allergic to eating oranges, Zookeeper would like to find the longest contiguous sequence of apples. Let f(l,r) be the longest contiguous sequence of apples in the substring s_{l}s_{l+1}\ldots s_{r}. Help Zookeeper find \sum_{l=1}^{n} \sum_{r=l}^{n} f(l,r), or the sum of f across all substrings.InputThe first line contains a single integer n (1 \leq n \leq 5 \cdot 10^5). The next line contains a binary string s of length n (s_i \in \{0,1\}) OutputPrint a single integer: \sum_{l=1}^{n} \sum_{r=l}^{n} f(l,r). ExamplesInput
4
0110
Output
12
Input
7
1101001
Output
30
Input
12
011100011100
Output
156
NoteIn the first test, there are ten substrings. The list of them (we let [l,r] be the substring s_l s_{l+1} \ldots s_r):  [1,1]: 0  [1,2]: 01  [1,3]: 011  [1,4]: 0110  [2,2]: 1  [2,3]: 11  [2,4]: 110  [3,3]: 1  [3,4]: 10  [4,4]: 0 The lengths of the longest contiguous sequence of ones in each of these ten substrings are 0,1,2,2,1,2,2,1,1,0 respectively. Hence, the answer is 0+1+2+2+1+2+2+1+1+0 = 12.
4
0110

12 
['binary search', 'data structures', 'divide and conquer', 'dp', 'two pointers', '*2400']