Iahub recently has learned Bubble Sort, an algorithm that is used to sort a permutation with n elements a1, a2, ..., an in ascending order. He is bored of this so simple algorithm, so he invents his own graph. The graph (let's call it G) initially has n vertices and 0 edges. During Bubble Sort execution, edges appear as described in the following algorithm (pseudocode). 
    
    
      
    procedure bubbleSortGraph()  
        build a graph G with n vertices and 0 edges  
        repeat  
            swapped = false  
            for i = 1 to n - 1 inclusive do:  
                if a[i] > a[i + 1] then  
                    add an undirected edge in G between a[i] and a[i + 1]  
                    swap( a[i], a[i + 1] )  
                    swapped = true  
                end if  
            end for  
        until not swapped   
        /* repeat the algorithm as long as swapped value is true. */   
    end procedure  
    

For a graph, an independent set is a set of vertices in a graph, no two of which are adjacent (so there are no edges between vertices of an independent set). A maximum independent set is an independent set which has maximum cardinality. Given the permutation, find the size of the maximum independent set of graph G, if we use such permutation as the premutation a in procedure bubbleSortGraph.

Input

The first line of the input contains an integer n (2 ≤ n ≤ 105). The next line contains n distinct integers a1, a2, ..., an (1 ≤ ai ≤ n).

Output

Output a single integer — the answer to the problem. 

Examples

Input

3
3 1 2


Output

2

Note

Consider the first example. Bubble sort swaps elements 3 and 1. We add edge (1, 3). Permutation is now [1, 3, 2]. Then bubble sort swaps elements 3 and 2. We add edge (2, 3). Permutation is now sorted. We have a graph with 3 vertices and 2 edges (1, 3) and (2, 3). Its maximal independent set is [1, 2].
100
36 48 92 87 28 85 42 10 44 41 39 3 79 9 14 56 1 16 46 35 93 8 82 26 100 59 60 2 96 52 13 98 70 81 71 94 54 91 17 88 33 30 19 50 18 73 65 29 78 21 61 7 99 97 45 89 57 27 76 11 49 72 84 69 43 62 4 22 75 6 66 83 38 34 86 15 40 51 37 74 67 31 20 63 77 80 12 53 5 25 58 90 68 24 64 23 95 32 55 47
 5
4 2 1 3 5
 10
1 9 8 10 2 3 4 6 5 7
 50
12 24 42 43 36 3 40 29 7 34 10 13 28 9 35 23 25 21 19 4 20 18 11 38 41 48 6 46 33 17 31 37 2 30 32 44 45 5 47 49 16 15 50 27 26 14 39 22 1 8

16
 3
 6
 13

// clang-format off
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;

#ifndef godfather
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
#endif

#define int long long
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef gp_hash_table<int, int> umap;
typedef tree<int, null_type, less<int>, rb_tree_tag,
        tree_order_statistics_node_update> oset;
typedef pair<pii, int> piii;
typedef vector<int> vi;
typedef vector<pii> vii;

#define INF 10000000000000000
#define inf 1000000000
#define MOD  1000000007
#define PI 3.1415926535897932385

#define pb push_back
#define bitc __builtin_popcountll
#define mp make_pair
#define all(ar) ar.begin(), ar.end()

#define fr(i, a, b) for (int i = (a), _b = (b); i <= _b; i++)
#define rep(i, n) for (int i = 0, _n = (n); i < _n; i++)
#define repr(i, n) for (int i = n - 1; i >= 0; i--)
#define frr(i, a, b) for (int i = (a), _b = (b); i >= _b; i--)
#define foreach(it, ar) for (auto it = ar.begin(); it != ar.end(); it++)
#define fil(ar, val) memset(ar, val, sizeof(ar))  // 0x3f for inf, 0x80 for -INF can also use with pairs

#ifdef godfather
template<typename T>
void __p(T a) { cout << a << " "; }
template<typename T>
void __p(std::vector<T> a) { cout << "{ "; for (auto p : a) __p(p); cout << "}"; }
template<typename T, typename F>
void __p(pair<T, F> a) { cout << "{ "; __p(a.first); __p(a.second); cout << "}"; }
template<typename T, typename ...Arg>
void __p(T a1, Arg ...a) { __p(a1); __p(a...); }
template<typename Arg1>
void __f(const char *name, Arg1 &&arg1) {
    cout<<name<<" : ";__p(arg1);cout<<endl;
}
template<typename Arg1, typename ... Args>
void __f(const char *names, Arg1 &&arg1, Args &&... args) {
    int bracket=0,i=0;
    for(; ;i++)
        if(names[i]==','&&bracket==0)
            break;
        else if(names[i]=='(')
            bracket++;
        else if(names[i]==')')
            bracket--;
    const char *comma=names+i;
    cout.write(names,comma-names)<<" : ";
    __p(arg1);
    cout<<"| ";
    __f(comma+1,args...);
}
#define trace(...) cout<<"Line:"<<__LINE__<<" "; __f(#__VA_ARGS__, __VA_ARGS__)
int begtime = clock();
#define end_routine() cout << "\n\nTime elapsed: " << (clock() - begtime)*1000/CLOCKS_PER_SEC << " ms\n\n";
#else
#define trace(...)
#define end_routine()
#endif

mt19937 rng32(chrono::steady_clock::now().time_since_epoch().count());
#define rand(l, r) uniform_int_distribution<int>(l, r)(rng32)
inline bool equals(double a, double b) { return fabs(a - b) < 1e-9; }
ll modpow(ll b, ll e, ll mod=MOD) {
    ll ans=1; for(;e;b=b*b%mod,e/=2) if(e&1) ans=ans*b%mod; return ans; }

ld modp(ld b, ll e) {
    ld ans=1; for(;e;b=b*b,e/=2) if(e&1) ans=ans*b; return ans; }

void solve()
{
    // START
    ll n;
    cin>>n;
    vector<ll> arr(n), vec(n);
    rep(i,n){
        cin>>arr[i];
        // vec[i]=arr[i];
    }
    // sort(all(vec));
    ll ans=1;
    ll l=0;
    for(ll i=1;i<n;i++){
        if(arr[i]<arr[i-1]){
            l=i;
        }
        ans=max(ans, i-l+1);
    }
    cout<<ans<<endl;


    // END
}

signed main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0), cout.tie(0), cout.precision(15);   cout<<fixed;
    #ifdef godfather
        cin.exceptions(cin.failbit);
        freopen("input.txt", "r", stdin);
        freopen("output.txt", "w", stdout);
    #endif
    int t=1;
    // cin>>t;
    fr(i,1,t)
    {
        solve();
    }
    end_routine();
}