[CF1333C]Eugene and an array

【原题】

Eugene likes working with arrays. And today he needs your help in solving one challenging task.

An array cc is a subarray of an array bb if cc can be obtained from bb by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.

Let's call a nonempty array good if for every nonempty subarray of this array, sum of the elements of this subarray is nonzero. For example, array −1,2,−3 is good, as all arrays −1, −1,2, −1,2,−3, 2, 2,−3, −3 have nonzero sums of elements. However, array −1,2,−1,−3 isn't good, as his subarray −1,2,−1 has sum of elements equal to 00.

Help Eugene to calculate the number of nonempty good subarrays of a given array aa.

 

Input

The first line of the input contains a single integer nn (1≤n≤2×1051≤n≤2×105) — the length of array aa.

The second line of the input contains nn integers a1,a2,…,an (−109≤ai≤109−109≤ai≤109) — the elements of aa.

 

Output

Output a single integer — the number of good subarrays of a.

 

Examples

input

Copy

3
1 2 -3

output

5

input

3
41 -41 41

output

3

Note

In the first sample, the following subarrays are good: 1, 1,2, 2, 2,−3, −3. However, the subarray 1,2,−3 isn't good, as its subarray 1,2,−3 has sum of elements equal to 0.

In the second sample, three subarrays of size 1 are the only good subarrays. At the same time, the subarray 41,−41,41 isn't good, as its subarray 41,−41 has sum of elements equal to 0.

【思路】

前缀和， map记录前缀和是否出现过及其最后出现位置， num记录最后不可行位置。

#include <algorithm>
#include <cmath>
#include <cstdio>
#include <cstring>
#include <list>
#include <map>
#include <iostream>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <vector>
#include <iomanip>
#define LL long long
#define inf 0x3f3f3f3f
#define INF 0x3f3f3f3f3f3f
#define PI 3.1415926535898
#define F first
#define S second
#define lson  rt << 1
#define rson  rt << 1 | 1
using namespace std;

const int maxn = 2e5 + 7;
const int maxm = 1e4 + 7;
int n, m;
LL a[maxn], sum[maxn];
map<LL, int> mp;

LL read()
{
    LL x = 0, f = 1;char ch = getchar();
    while (ch < '0' || ch>'9') { if (ch == '-')f = -1;ch = getchar(); }
    while (ch >= '0' && ch <= '9') { x = x * 10 + ch - '0';ch = getchar(); }
    return x * f;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    n = read();
    for (int i = 1; i <= n; i++)
    {
        a[i] = read();
        sum[i] = sum[i - 1] + a[i];
    }
    LL cnt = 0;
    int num = 0;
    mp[0] = 0;
    for (int i = 1; i <= n; i++)
    {
        if (mp.count(sum[i])) num = max(mp[sum[i]] + 1, num);
        mp[sum[i]] = i;
        cnt += i - num;
    }
    cout << cnt << endl;
}