F. Fruit Sequences
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Zookeeper 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.

Input

The 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 $n$ $(s_i \in \{0,1\})$

Output

Print a single integer: $\sum_{l=1}^{n} \sum_{r=l}^{n} f(l,r)$.

Examples
Input
4
0110

Output
12

Input
7
1101001

Output
30

Input
12
011100011100

Output
156

Note

In 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 $0+1+2+2+1+2+2+1+1+0 = 12$.