Mr. Chanek gives you a sequence a indexed from 1 to n. Define f(a) as the number of indices where a_i = i. 

You can pick an element from the current sequence and remove it, then concatenate the remaining elements together. For example, if you remove the 3-rd element from the sequence [4, 2, 3, 1], the resulting sequence will be [4, 2, 1]. 

You want to remove some elements from a in order to maximize f(a), using zero or more operations. Find the largest possible f(a).

Input

The first line contains one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the initial length of the sequence.

The second line contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 2 ⋅ 10^5) — the initial sequence a.

Output

Output an integer denoting the largest f(a) that can be obtained by doing zero or more operations.

Examples

Input


7
2 1 4 2 5 3 7


Output


3


Input


4
4 2 3 1


Output


2

Note

In the first example, f(A) = 3 by doing the following operations.

[2,1,4,2,5,3,7] → [2,1,2,5,3,7] → [1,2,5,3,7] → [1,2,5,3] → [1,2,3]

In the second example, f(A) = 2 and no additional operation is needed.
#include <bits/stdc++.h>
using namespace std;
 
using ll = long long;
using db = long double; // or double, if TL is tight
using str = string; // yay python! 

using pi = pair<int,int>;
using pl = pair<ll,ll>;
using pd = pair<db,db>;

using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<db>;
using vs = vector<str>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;

#define tcT template<class T
#define tcTU tcT, class U
// ^ lol this makes everything look weird but I'll try it
tcT> using V = vector<T>; 
tcT, size_t SZ> using AR = array<T,SZ>; 
tcT> using PR = pair<T,T>;

// pairs
#define mp make_pair
#define f first
#define s second

// vectors
// oops size(x), rbegin(x), rend(x) need C++17
#define sz(x) int((x).size())
#define bg(x) begin(x)
#define all(x) bg(x), end(x)
#define rall(x) x.rbegin(), x.rend() 
#define sor(x) sort(all(x)) 
#define rsz resize
#define ins insert 
#define ft front()
#define bk back()
#define pb push_back
#define eb emplace_back 
#define pf push_front
#define rtn return

#define lb lower_bound
#define ub upper_bound
tcT> int lwb(V<T>& a, const T& b) { return int(lb(all(a),b)-bg(a)); }
tcT> int upb(V<T>& a, const T& b) { return int(ub(all(a),b)-bg(a)); }

// loops
#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define rep(a) F0R(_,a)
#define each(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5;
const ll BIG = 1e18; // not too close to LLONG_MAX
const db PI = acos((db)-1);
const int dx[4]{1,0,-1,0}, dy[4]{0,1,0,-1}; // for every grid problem!!
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 
template<class T> using pqg = priority_queue<T,vector<T>,greater<T>>;

// bitwise ops
// also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html
constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set
constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until USACO updates ...
    return x == 0 ? 0 : 31-__builtin_clz(x); } // floor(log2(x)) 
constexpr int p2(int x) { return 1<<x; }
constexpr int msk2(int x) { return p2(x)-1; }

ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down

tcT> bool ckmin(T& a, const T& b) {
    return b < a ? a = b, 1 : 0; } // set a = min(a,b)
tcT> bool ckmax(T& a, const T& b) {
    return a < b ? a = b, 1 : 0; }

tcTU> T fstTrue(T lo, T hi, U f) {
    hi ++; assert(lo <= hi); // assuming f is increasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo)/2;
        f(mid) ? hi = mid : lo = mid+1; 
    } 
    return lo;
}
tcTU> T lstTrue(T lo, T hi, U f) {
    lo --; assert(lo <= hi); // assuming f is decreasing
    while (lo < hi) { // find first index such that f is true 
        T mid = lo+(hi-lo+1)/2;
        f(mid) ? lo = mid : hi = mid-1;
    } 
    return lo;
}
tcT> void remDup(vector<T>& v) { // sort and remove duplicates
    sort(all(v)); v.erase(unique(all(v)),end(v)); }
tcTU> void erase(T& t, const U& u) { // don't erase
    auto it = t.find(u); assert(it != end(t));
    t.erase(it); } // element that doesn't exist from (multi)set

#define tcTUU tcT, class ...U

inline namespace Helpers {
    //////////// is_iterable
    // https://stackoverflow.com/questions/13830158/check-if-a-variable-type-is-iterable
    // this gets used only when we can call begin() and end() on that type
    tcT, class = void> struct is_iterable : false_type {};
    tcT> struct is_iterable<T, void_t<decltype(begin(declval<T>())),
                                      decltype(end(declval<T>()))
                                     >
                           > : true_type {};
    tcT> constexpr bool is_iterable_v = is_iterable<T>::value;

    //////////// is_readable
    tcT, class = void> struct is_readable : false_type {};
    tcT> struct is_readable<T,
            typename std::enable_if_t<
                is_same_v<decltype(cin >> declval<T&>()), istream&>
            >
        > : true_type {};
    tcT> constexpr bool is_readable_v = is_readable<T>::value;

    //////////// is_printable
    // // https://nafe.es/posts/2020-02-29-is-printable/
    tcT, class = void> struct is_printable : false_type {};
    tcT> struct is_printable<T,
            typename std::enable_if_t<
                is_same_v<decltype(cout << declval<T>()), ostream&>
            >
        > : true_type {};
    tcT> constexpr bool is_printable_v = is_printable<T>::value;
}

inline namespace Input {
    tcT> constexpr bool needs_input_v = !is_readable_v<T> && is_iterable_v<T>;
    tcTUU> void re(T& t, U&... u);
    tcTU> void re(pair<T,U>& p); // pairs

    // re: read
    tcT> typename enable_if<is_readable_v<T>,void>::type re(T& x) { cin >> x; } // default
    tcT> void re(complex<T>& c) { T a,b; re(a,b); c = {a,b}; } // complex
    tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i); // ex. vectors, arrays
    tcTU> void re(pair<T,U>& p) { re(p.f,p.s); }
    tcT> typename enable_if<needs_input_v<T>,void>::type re(T& i) {
        each(x,i) re(x); }
    tcTUU> void re(T& t, U&... u) { re(t); re(u...); } // read multiple

    // rv: resize and read vectors
    void rv(size_t) {}
    tcTUU> void rv(size_t N, V<T>& t, U&... u);
    template<class...U> void rv(size_t, size_t N2, U&... u);
    tcTUU> void rv(size_t N, V<T>& t, U&... u) {
        t.rsz(N); re(t);
        rv(N,u...); }
    template<class...U> void rv(size_t, size_t N2, U&... u) {
        rv(N2,u...); }

    // dumb shortcuts to read in ints
    void decrement() {} // subtract one from each
    tcTUU> void decrement(T& t, U&... u) { --t; decrement(u...); }
    #define ints(...) int __VA_ARGS__; re(__VA_ARGS__);
    #define int1(...) ints(__VA_ARGS__); decrement(__VA_ARGS__);
}

inline namespace ToString {
    tcT> constexpr bool needs_output_v = !is_printable_v<T> && is_iterable_v<T>;

    // ts: string representation to print
    tcT> typename enable_if<is_printable_v<T>,str>::type ts(T v) {
        stringstream ss; ss << fixed << setprecision(15) << v;
        return ss.str(); } // default
    tcT> str bit_vec(T t) { // bit vector to string
        str res = "{"; F0R(i,sz(t)) res += ts(t[i]);
        res += "}"; return res; }
    str ts(V<bool> v) { return bit_vec(v); }
    template<size_t SZ> str ts(bitset<SZ> b) { return bit_vec(b); } // bit vector
    tcTU> str ts(pair<T,U> p); // pairs
    tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v); // vectors, arrays
    tcTU> str ts(pair<T,U> p) { return "("+ts(p.f)+", "+ts(p.s)+")"; }
    tcT> typename enable_if<is_iterable_v<T>,str>::type ts_sep(T v, str sep) {
        // convert container to string w/ separator sep
        bool fst = 1; str res = "";
        for (const auto& x: v) {
            if (!fst) res += sep;
            fst = 0; res += ts(x);
        }
        return res;
    }
    tcT> typename enable_if<needs_output_v<T>,str>::type ts(T v) {
        return "{"+ts_sep(v,", ")+"}"; }

    // for nested DS
    template<int, class T> typename enable_if<!needs_output_v<T>,vs>::type 
      ts_lev(const T& v) { return {ts(v)}; }
    template<int lev, class T> typename enable_if<needs_output_v<T>,vs>::type 
      ts_lev(const T& v) {
        if (lev == 0 || !sz(v)) return {ts(v)};
        vs res;
        for (const auto& t: v) {
            if (sz(res)) res.bk += ",";
            vs tmp = ts_lev<lev-1>(t);
            res.ins(end(res),all(tmp));
        }
        F0R(i,sz(res)) {
            str bef = " "; if (i == 0) bef = "{";
            res[i] = bef+res[i];
        }
        res.bk += "}";
        return res;
    }
}

inline namespace Output {
    template<class T> void pr_sep(ostream& os, str, const T& t) { os << ts(t); }
    template<class T, class... U> void pr_sep(ostream& os, str sep, const T& t, const U&... u) {
        pr_sep(os,sep,t); os << sep; pr_sep(os,sep,u...); }
    // print w/ no spaces
    template<class ...T> void pr(const T&... t) { pr_sep(cout,"",t...); } 
    // print w/ spaces, end with newline
    void ps() { cout << "\n"; }
    template<class ...T> void ps(const T&... t) { pr_sep(cout," ",t...); ps(); } 
    // debug to cerr
    template<class ...T> void dbg_out(const T&... t) {
        pr_sep(cerr," | ",t...); cerr << endl; }
    void loc_info(int line, str names) {
        cerr << "Line(" << line << ") -> [" << names << "]: "; }
    template<int lev, class T> void dbgl_out(const T& t) {
        cerr << "\n\n" << ts_sep(ts_lev<lev>(t),"\n") << "\n" << endl; }
    #ifdef LOCAL
        #define dbg(...) loc_info(__LINE__,#__VA_ARGS__), dbg_out(__VA_ARGS__)
        #define dbgl(lev,x) loc_info(__LINE__,#x), dbgl_out<lev>(x)
    #else // don't actually submit with this
        #define dbg(...) 0
        #define dbgl(lev,x) 0
    #endif

    const clock_t beg = clock();
    #define dbg_time() dbg((db)(clock()-beg)/CLOCKS_PER_SEC)
}

inline namespace FileIO {
    void setIn(str s)  { freopen(s.c_str(),"r",stdin); }
    void setOut(str s) { freopen(s.c_str(),"w",stdout); }
    void setIO(str s = "") {
        cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams
        // cin.exceptions(cin.failbit);
        // throws exception when do smth illegal
        // ex. try to read letter into int
        if (sz(s)) setIn(s+".in"), setOut(s+".out"); // for old USACO
    }
}

struct fenwick {
    vector<int> d;
    void init(int n) {
        d.resize(n);
    }
    int getmax(int i) {
        int ans = 0;
        for (; i >= 0; i = (i & (i + 1)) - 1) {
            ans = max(ans, d[i]);
        }
        return ans;
    }
    void update(int i, int val) {
        for (; i < sz(d); i |= (i + 1)) {
            d[i] = max(d[i], val);
        }
    }
};


struct fenwick2D {
    vector<vector<int>> cords;
    vector<fenwick> st;
    void init(int n) {
        cords.resize(n);
        st.resize(n);
    }
    void prepush(int i, int x) {
        int ni = i;
        for (; i < sz(cords); i |= (i + 1)) {
            cords[i].pb(x);
        }
        i = ni;
        for (; i >= 0; i = (i & (i + 1)) - 1) {
            cords[i].pb(x);
        }
    }
    void pushall() {
        for (int i = 0; i < sz(cords); i++) {
            sort(all(cords[i]));
            cords[i].resize(distance(cords[i].begin(), unique(all(cords[i]))));
            st[i].init(sz(cords[i]));
        }
    }
    void update(int i, int x, int val) {
        for (; i < sz(cords); i |= (i + 1)) {
            int pos = lower_bound(all(cords[i]), x) - cords[i].begin();
            st[i].update(pos, val);
        }
    }
    int getmax(int i, int x) {
        int ans = 0;
        for (; i >= 0; i = (i & (i + 1)) - 1) {
            int pos = lower_bound(all(cords[i]), x) - cords[i].begin();
            ans = max(ans, st[i].getmax(pos));
        }
        return ans;
    }
};


const int mx = 200005;


struct Eff{

int n;
int a[mx]{};



vector<pair<pi, int>> all_upds;

// void UPD_init(int X, int Y){
//    return;
// }
// void UPD(int X, int Y, int val){
//    all_upds.pb(mp(mp(X, Y), val));
// }

// int QUERY(int X, int Y){
//    int res = 0;
//    for(auto u: all_upds){
//        if(u.f.f <= X && u.f.s <= Y){
//            ckmax(res, u.s);
//        }
//    }
//    return res;
// }

fenwick2D FEN;

 void UPD_init(int X, int Y){
     FEN.prepush(X, Y);
 }

 void UPD(int X, int Y, int val){
     FEN.update(X, Y, val);
 }

 int QUERY(int X, int Y){
     return FEN.getmax(X, Y);
 }


void solve(){
    cin >> n;
    for(int i = 1; i <= n; i++){
        cin >> a[i];
    }

    FEN.init(2*mx+5);

     UPD_init(0, 0);

    for(int i = 1; i <= n; i++){
        int Lx = 0;
        int Rx = a[i];
        int Ly = 0;
        int Ry = i-a[i];

        if(Ry < 0) continue;

        UPD_init(Rx, Ry);
        // dbg(res+1, Rx, Ry);
        // UPD_init(Rx, Ry);
        // ckmax(ans, res+1);
    }
    FEN.pushall();


    //UPDATE 0, 0 to value 0
    UPD(0, 0, 0);

    int ans = 0;
    for(int i = 1; i <= n; i++){
        int Lx = 0;
        int Rx = a[i];
        int Ly = 0;
        int Ry = i-a[i];

        if(Ry < 0) continue;

        int res = QUERY(Rx, Ry);
        // dbg(res+1, Rx, Ry);
        UPD(Rx, Ry, res+1);
        ckmax(ans, res+1);
    }
    ps(ans);
}  

};


int main() {
    setIO();
    Eff e;
    e.solve();
    // you should actually read the stuff at the bottom
}

/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?)
    * do smth instead of nothing and stay organized
    * WRITE STUFF DOWN
    * DON'T GET STUCK ON ONE APPROACH
*/
