DZY Loves Sequences

/**
 *    author:  compounding
 *    created: 2024-12-08 14:46:24
 **/
#include <bits/stdc++.h>
using namespace std;
mt19937_64 RNG(chrono::steady_clock::now().time_since_epoch().count());
#define NeedForSpeed                  \
    ios_base::sync_with_stdio(false); \
    cin.tie(NULL);                    \
    cout.tie(NULL);
#define int long long
#define all(x) (x).begin(), (x).end()
typedef vector<int> vi;
typedef vector<bool> vb;
typedef vector<vi> vvi;
typedef vector<pair<int, int>> vpi;
#define f first
#define s second
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define endl "\n"
const int mod = 1000000007;
int gcd(int a, int b) { return b == 0 ? a : gcd(b, a % b); }
void solve()
{
    // TODO: LIS, with atmost 1 change to make it strictly increasing
    int n;
    cin >> n;
    vi a(n);
    for (int i = 0; i < n; i++)
    {
        cin >> a[i];
    }
    vi lis_ending_at_i(n, 1);
    vi lis_starting_from_i(n, 1);
    vi L; // seq array
    L.push_back(a[0]);
    for (int i = 0; i < n; i++)
    {
        auto it = lower_bound(all(L), a[i]);
        int length = it - L.begin();
        lis_ending_at_i[i] = length + 1;
        if (it == L.end())
        {
            L.push_back(a[i]);
        }
        else
        {
            *it = a[i];
        }
    }
    vi R;
    R.push_back(a[n - 1]);
    for (int i = n - 1; i >= 0; i--)
    {
        auto it = lower_bound(all(R), a[i]);
        int length = it - R.begin();
        lis_starting_from_i[i] = length + 1;
        if (it == R.end())
        {
            R.push_back(a[i]);
        }
        else
        {
            *it = a[i];
        }
    }
    int ans = 1;
    for (int i = 0; i < n; i++)
    {
        if (i && i < n - 1)
        {
            if (a[i - 1] + 1 < a[i + 1])
            {
                // we change the element at i, to (a[i-1]+1)
                ans = max({ans, lis_ending_at_i[i - 1] + lis_starting_from_i[i + 1] + 1});
            }
        }
        if (i)
        {
            ans = max(ans, lis_ending_at_i[i - 1] + 1);
        }
        if (i < n - 1)
        {
            ans = max(ans, lis_starting_from_i[i - 1] + 1);
        }
    }
    cout << ans + 1 << endl;
    return;
}

signed main()
{
    NeedForSpeed;
    int t = 1;
    // cin >> t;
    while (t--)
    {
        solve();
    }
    return 0;
}