#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template<typename T> class UpdateSet
{
private:
    using ptt = pair<T,T>;
    T inf;
public:
    //1の区間をsetで保持
    set<ptt> st;
    UpdateSet() : inf(numeric_limits<T>::max()){};
    //[l,r)をk(0,1)に更新
    void update(T l,T r,int k){
        T lb = l, rb = r;
        while(1){
            auto it = st.lower_bound(ptt(l,-inf));
            if(it == st.end()){
                break;
            }
            ptt p = *it;
            if(p.fi > r){
                break;
            }
            st.erase(it);
            if(p.se > r){
                rb = max(rb, p.se);
                if(!k) st.insert(ptt(r,p.se));
                break;
            }
        }
        auto it = st.lower_bound(ptt(l,-inf));
        if(it != st.begin()){
            --it;
            ptt p = *it;
            if(p.se >= l){
                st.erase(it);
                if(!k) st.insert(ptt(p.fi,l));
                lb = min(lb, p.fi);
            }
            if(p.se > r){
                if(!k) st.insert(ptt(r,p.se));
                rb = max(rb, p.se);
            }
        }
        if(k){
            st.insert(ptt(lb,rb));
        }
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vi x(n);
    rep(i,n){
        cin >> x[i];
    }
    UpdateSet<int> us;
    bool ed = false;
    rep(i,n){
        if(ed){
            cout << "No\n";
            continue;
        }
        auto& st = us.st;
        auto it = st.lower_bound(P(x[i],INF));
        if(it == st.begin()){
            cout << "Yes\n";
            us.update(x[i],x[i]+1,1);
        }else{
            it--;
            if(x[i] < it->se){
                int ch = it->fi;
                if(ch == 1){
                    if(x[i] != it->se-1 || len(st) != 1){
                        cout << "No\n";
                        continue;
                    }else{
                        ed = true;
                    }
                }
                cout << "Yes\n";
                us.update(ch,x[i]+1,0);
                us.update(ch-1,ch,1);
            }else{
                cout << "Yes\n";
                us.update(x[i],x[i]+1,1);
            }
        }
    }
    return 0;
}


### Prompt

Please formulate a Cpp solution to the following problem:

Example

Input

6
2
3
1
1
4
2


Output

Yes
Yes
Yes
No
Yes
No

### Response

```cpp
#include <bits/stdc++.h>
#define ll long long
#define INF 1000000005
#define MOD 1000000007
#define EPS 1e-10
#define rep(i,n) for(int i=0;i<(int)(n);++i)
#define rrep(i,n) for(int i=(int)(n)-1;i>=0;--i)
#define srep(i,s,t) for(int i=(int)(s);i<(int)(t);++i)
#define each(a,b) for(auto& (a): (b))
#define all(v) (v).begin(),(v).end()
#define len(v) (int)(v).size()
#define zip(v) sort(all(v)),v.erase(unique(all(v)),v.end())
#define cmx(x,y) x=max(x,y)
#define cmn(x,y) x=min(x,y)
#define fi first
#define se second
#define pb push_back
#define show(x) cout<<#x<<" = "<<(x)<<endl
#define spair(p) cout<<#p<<": "<<p.fi<<" "<<p.se<<endl
#define sar(a,n) cout<<#a<<":";rep(pachico,n)cout<<" "<<a[pachico];cout<<endl
#define svec(v) cout<<#v<<":";rep(pachico,v.size())cout<<" "<<v[pachico];cout<<endl
#define svecp(v) cout<<#v<<":";each(pachico,v)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl
#define sset(s) cout<<#s<<":";each(pachico,s)cout<<" "<<pachico;cout<<endl
#define smap(m) cout<<#m<<":";each(pachico,m)cout<<" {"<<pachico.first<<":"<<pachico.second<<"}";cout<<endl

using namespace std;

typedef pair<int,int> P;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<double> vd;
typedef vector<P> vp;
typedef vector<string> vs;

const int MAX_N = 100005;

template<typename T> class UpdateSet
{
private:
    using ptt = pair<T,T>;
    T inf;
public:
    //1の区間をsetで保持
    set<ptt> st;
    UpdateSet() : inf(numeric_limits<T>::max()){};
    //[l,r)をk(0,1)に更新
    void update(T l,T r,int k){
        T lb = l, rb = r;
        while(1){
            auto it = st.lower_bound(ptt(l,-inf));
            if(it == st.end()){
                break;
            }
            ptt p = *it;
            if(p.fi > r){
                break;
            }
            st.erase(it);
            if(p.se > r){
                rb = max(rb, p.se);
                if(!k) st.insert(ptt(r,p.se));
                break;
            }
        }
        auto it = st.lower_bound(ptt(l,-inf));
        if(it != st.begin()){
            --it;
            ptt p = *it;
            if(p.se >= l){
                st.erase(it);
                if(!k) st.insert(ptt(p.fi,l));
                lb = min(lb, p.fi);
            }
            if(p.se > r){
                if(!k) st.insert(ptt(r,p.se));
                rb = max(rb, p.se);
            }
        }
        if(k){
            st.insert(ptt(lb,rb));
        }
    }
};

int main()
{
    cin.tie(0);
    ios::sync_with_stdio(false);
    int n;
    cin >> n;
    vi x(n);
    rep(i,n){
        cin >> x[i];
    }
    UpdateSet<int> us;
    bool ed = false;
    rep(i,n){
        if(ed){
            cout << "No\n";
            continue;
        }
        auto& st = us.st;
        auto it = st.lower_bound(P(x[i],INF));
        if(it == st.begin()){
            cout << "Yes\n";
            us.update(x[i],x[i]+1,1);
        }else{
            it--;
            if(x[i] < it->se){
                int ch = it->fi;
                if(ch == 1){
                    if(x[i] != it->se-1 || len(st) != 1){
                        cout << "No\n";
                        continue;
                    }else{
                        ed = true;
                    }
                }
                cout << "Yes\n";
                us.update(ch,x[i]+1,0);
                us.update(ch-1,ch,1);
            }else{
                cout << "Yes\n";
                us.update(x[i],x[i]+1,1);
            }
        }
    }
    return 0;
}


```