#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.141592653589793238462643383279;
const vector<ll>four{0,1,0,-1,0};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto &i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
inline  ll gcd(ll a,ll b){if(!a||!b)return 0;while(b){ll c=b;b=a%b;a=c;}return a;}
inline  ll lcm(ll a,ll b){if(!a||!b)return 0;return a*b/gcd(a,b);}
template<class T> inline  T min(vector<T> &v){return *min_element(range(v));}
inline char min(string &v){return *min_element(range(v));}
template<class T> inline  T max(vector<T> &v){return *max_element(range(v));}
inline char max(string &v){return *max_element(range(v));}
inline  ll intpow(ll a,ll b){ll ans=1;for(ll i=1;b;i*=2){if(b&i){b^=i;ans*=a;}a*=a;}return ans;}
template<typename T>
inline  bool chmin(T &mn,const T &cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;}
template<typename T>
inline  bool chmax(T &mx,const T &cnt){if(mx<cnt){mx=cnt;return 1;}else return 0;}
template<class T> unordered_map<T,ll> press(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T,ll> press_map(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin>>a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ each(i, a) print(i); }
template<class T> void print(const vector<T> &vec);
template<class T, size_t size> void print(const array<T, size> &vec);
template<class T, class L> void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template <class T> inline void err(T t){cerr<<t<<'\n';}
template<class Head, class... Tail> inline void err(const Head &head, const Tail&... tail){ cerr<<head<<' '; err(tail...); }
inline void err(){cerr<<'\n';}
inline int first(const bool &i){return out(i?"first":"second");}
inline int yes(const bool &i){return out(i?"yes":"no");}
inline int Yes(const bool &i){return out(i?"Yes":"No");}
inline int YES(const bool &i){return out(i?"YES":"NO");}
inline int Yay(const bool &i){return out(i?"Yay!":":(");}
inline int Possible(const bool &i){return out(i?"Possible":"Impossible");}
inline int POSSIBLE(const bool &i){return out(i?"POSSIBLE":"IMPOSSIBLE");}
inline void Case(ll i){printf("Case #%lld: ",i);}


template<class T>
struct PartialSum{
    vector<T> data;
    PartialSum(const vector<T>& v): data(v.size() + 1){
        for(ll i = 0; i < v.size(); i++) data[i + 1] = data[i] + v[i];
    }
    T get(ll l, ll r) const {
        return data[r] - data[l];
    }
};
int main(){
    LL(n);
    VEC(ll,a,n);
    PartialSum<ll> s(a);
    unordered_map<ll,pll>minmax;
    rep(n+1){
        if(!minmax.count(s.data[i])){
            minmax[s.data[i]]={LINF,-LINF};
        }
        chmin(minmax[s.data[i]].first,i);
        chmax(minmax[s.data[i]].second,i);
    }
    ll ans=0;
    each(i,minmax)chmax(ans,i.second.second-i.second.first);
    out(ans);
}




### Prompt

Please formulate a CPP solution to the following problem:

Aiz, which is located in cyberspace, trades information with Wakamatsu. The two countries are developing their economies by exchanging useful data with each other. The two countries, whose national policy is philanthropy and equality, and above all, the old word of the Aizu region, "what must be done", conducts regular surveys of trade conditions.

In the survey, a table is given in which the value obtained by subtracting the outflow amount from the data inflow amount seen from Aiz country in byte units is calculated every 1 nanosecond. From that table, find the longest interval where the sum of the values ​​is zero. It is judged that the longer this section is, the more equality is maintained.

Given a table with trade status, write a program to find the length of the longest interval where the sum of the values ​​is zero.



Input

The input is given in the following format.


N
d1
d2
::
dN


The first row gives the number N (1 ≤ N ≤ 200000) of the values ​​written in the table. The next N rows are given the integer di (-109 ≤ di ≤ 109), which indicates the value written in row i of the table.

Output

The length of the longest section obtained from the table where the sum is 0 is output in one line. If such an interval does not exist, "0" is output on one line.

Examples

Input

5
18
102
-155
53
32


Output

3


Input

4
1
1
-1
-1


Output

4

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using ld=long double;
using ull=unsigned long long;
using uint=unsigned int;
using pcc=pair<char,char>;
using pii=pair<int,int>;
using pll=pair<ll,ll>;
using pdd=pair<double,double>;
using tuplis=pair<ll,pll>;
using tuplis2=pair<pll,ll>;
template<class T> using pq=priority_queue<T,vector<T>,greater<T>>;
const ll LINF=0x1fffffffffffffff;
const ll MINF=0x7fffffffffff;
const int INF=0x3fffffff;
const ll MOD=1000000007;
const ll MODD=998244353;
const ld DINF=numeric_limits<ld>::infinity();
const ld EPS=1e-9;
const ld PI=3.141592653589793238462643383279;
const vector<ll>four{0,1,0,-1,0};
#define _overload4(_1,_2,_3,_4,name,...) name
#define _overload3(_1,_2,_3,name,...) name
#define _rep1(n) for(ll i=0;i<n;++i)
#define _rep2(i,n) for(ll i=0;i<n;++i)
#define _rep3(i,a,b) for(ll i=a;i<b;++i)
#define _rep4(i,a,b,c) for(ll i=a;i<b;i+=c)
#define rep(...) _overload4(__VA_ARGS__,_rep4,_rep3,_rep2,_rep1)(__VA_ARGS__)
#define _rrep1(n) for(ll i=(n)-1;i>=0;i--)
#define _rrep2(i,n) for(ll i=(n)-1;i>=0;i--)
#define _rrep3(i,a,b) for(ll i=(b)-1;i>=(a);i--)
#define _rrep4(i,a,b,c) for(ll i=a+(b-a-1)/c*c;i>=a;i-=c)
#define rrep(...) _overload4(__VA_ARGS__,_rrep4,_rrep3,_rrep2,_rrep1)(__VA_ARGS__)
#define each(i,a) for(auto &i:a)
#define sum(...) accumulate(range(__VA_ARGS__),0LL)
#define dsum(...) accumulate(range(__VA_ARGS__),double(0))
#define _range(i) (i).begin(),(i).end()
#define _range2(i,k) (i).begin(),(i).begin()+k
#define _range3(i,a,b) (i).begin()+a,(i).begin()+b
#define range(...) _overload3(__VA_ARGS__,_range3,_range2,_range)(__VA_ARGS__)
#define _rrange(i) (i).rbegin(),(i).rend()
#define _rrange2(i,k) (i).rbegin(),(i).rbegin()+k
#define _rrange3(i,a,b) (i).rbegin()+a,(i).rbegin()+b
#define rrange(...) _overload3(__VA_ARGS__,_rrange3,_rrange2,_rrange)(__VA_ARGS__)
#define elif else if
#define unless(a) if(!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...) int __VA_ARGS__;in(__VA_ARGS__)
#define LL(...) ll __VA_ARGS__;in(__VA_ARGS__)
#define ULL(...) ull __VA_ARGS__;in(__VA_ARGS__)
#define STR(...) string __VA_ARGS__;in(__VA_ARGS__)
#define CHR(...) char __VA_ARGS__;in(__VA_ARGS__)
#define DBL(...) double __VA_ARGS__;in(__VA_ARGS__)
#define LD(...) ld __VA_ARGS__;in(__VA_ARGS__)
#define vec(type,name,...) vector<type> name(__VA_ARGS__)
#define VEC(type,name,size) vector<type> name(size);in(name)
#define vv(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__))
#define VV(type,name,h,...) vector<vector<type>>name(h,vector<type>(__VA_ARGS__));in(name)
#define vvv(type,name,h,w,...) vector<vector<vector<type>>>name(h,vector<vector<type>>(w,vector<type>(__VA_ARGS__)))
inline  ll gcd(ll a,ll b){if(!a||!b)return 0;while(b){ll c=b;b=a%b;a=c;}return a;}
inline  ll lcm(ll a,ll b){if(!a||!b)return 0;return a*b/gcd(a,b);}
template<class T> inline  T min(vector<T> &v){return *min_element(range(v));}
inline char min(string &v){return *min_element(range(v));}
template<class T> inline  T max(vector<T> &v){return *max_element(range(v));}
inline char max(string &v){return *max_element(range(v));}
inline  ll intpow(ll a,ll b){ll ans=1;for(ll i=1;b;i*=2){if(b&i){b^=i;ans*=a;}a*=a;}return ans;}
template<typename T>
inline  bool chmin(T &mn,const T &cnt){if(mn>cnt){mn=cnt;return 1;}else return 0;}
template<typename T>
inline  bool chmax(T &mx,const T &cnt){if(mx<cnt){mx=cnt;return 1;}else return 0;}
template<class T> unordered_map<T,ll> press(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); unordered_map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
template<class T> map<T,ll> press_map(vector<T> &a){ auto b = a; sort(range(b)); b.erase(unique(range(b)), b.end()); map<T,ll> ans; rep(b.size()) ans[b[i]] = i; each(i, a) i = ans[i]; return ans; }
inline int scan(){ return getchar(); }
inline void scan(int &a){ scanf("%d", &a); }
inline void scan(unsigned &a){ scanf("%u", &a); }
inline void scan(long &a){ scanf("%ld", &a); }
inline void scan(long long &a){ scanf("%lld", &a); }
inline void scan(unsigned long long &a){ scanf("%llu", &a); }
inline void scan(char &a){ cin >> a; }
inline void scan(float &a){ scanf("%f", &a); }
inline void scan(double &a){ scanf("%lf", &a); }
inline void scan(long double &a){ scanf("%Lf", &a); }
inline void scan(vector<bool> &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } }
inline void scan(char a[]){ scanf("%s", a); }
inline void scan(string &a){ cin >> a; }
template<class T> inline void scan(vector<T> &vec);
template<class T, size_t size> inline void scan(array<T, size> &vec);
template<class T, class L> inline void scan(pair<T, L> &p);
template<class T, size_t size> inline void scan(T (&vec)[size]);
template<class T> inline void scan(vector<T> &vec){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(deque<T> &vec){ for(auto &i : vec) scan(i); }
template<class T, size_t size> inline void scan(array<T, size> &vec){ for(auto &i : vec) scan(i); }
template<class T, class L> inline void scan(pair<T, L> &p){ scan(p.first); scan(p.second); }
template<class T, size_t size> inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); }
template<class T> inline void scan(T &a){ cin>>a; }
inline void in(){}
template <class Head, class... Tail> inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); }
inline void print(){ putchar(' '); }
inline void print(const bool &a){ printf("%d", a); }
inline void print(const int &a){ printf("%d", a); }
inline void print(const unsigned &a){ printf("%u", a); }
inline void print(const long &a){ printf("%ld", a); }
inline void print(const long long &a){ printf("%lld", a); }
inline void print(const unsigned long long &a){ printf("%llu", a); }
inline void print(const char &a){ printf("%c", a); }
inline void print(const char a[]){ printf("%s", a); }
inline void print(const float &a){ printf("%.15f", a); }
inline void print(const double &a){ printf("%.15f", a); }
inline void print(const long double &a){ printf("%.15Lf", a); }
inline void print(const string &a){ each(i, a) print(i); }
template<class T> void print(const vector<T> &vec);
template<class T, size_t size> void print(const array<T, size> &vec);
template<class T, class L> void print(const pair<T, L> &p);
template<class T, size_t size> inline void print(const T (&vec)[size]);
template<class T> void print(const vector<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T> void print(const deque<T> &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, size_t size> void print(const array<T, size> &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } }
template<class T, class L> void print(const pair<T, L> &p){ print(p.first); putchar(' '); print(p.second); }
template<class T, size_t size> inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } }
template<class T> inline void print(const T &a){ cout << a; }
inline int out(){ putchar('\n'); return 0; }
template<class T> inline int out(const T &t){ print(t); putchar('\n'); return 0; }
template<class Head, class... Tail> inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; }
template <class T> inline void err(T t){cerr<<t<<'\n';}
template<class Head, class... Tail> inline void err(const Head &head, const Tail&... tail){ cerr<<head<<' '; err(tail...); }
inline void err(){cerr<<'\n';}
inline int first(const bool &i){return out(i?"first":"second");}
inline int yes(const bool &i){return out(i?"yes":"no");}
inline int Yes(const bool &i){return out(i?"Yes":"No");}
inline int YES(const bool &i){return out(i?"YES":"NO");}
inline int Yay(const bool &i){return out(i?"Yay!":":(");}
inline int Possible(const bool &i){return out(i?"Possible":"Impossible");}
inline int POSSIBLE(const bool &i){return out(i?"POSSIBLE":"IMPOSSIBLE");}
inline void Case(ll i){printf("Case #%lld: ",i);}


template<class T>
struct PartialSum{
    vector<T> data;
    PartialSum(const vector<T>& v): data(v.size() + 1){
        for(ll i = 0; i < v.size(); i++) data[i + 1] = data[i] + v[i];
    }
    T get(ll l, ll r) const {
        return data[r] - data[l];
    }
};
int main(){
    LL(n);
    VEC(ll,a,n);
    PartialSum<ll> s(a);
    unordered_map<ll,pll>minmax;
    rep(n+1){
        if(!minmax.count(s.data[i])){
            minmax[s.data[i]]={LINF,-LINF};
        }
        chmin(minmax[s.data[i]].first,i);
        chmax(minmax[s.data[i]].second,i);
    }
    ll ans=0;
    each(i,minmax)chmax(ans,i.second.second-i.second.first);
    out(ans);
}




```