Dynamic Programming / Increasing Subsequence

#include <bits/stdc++.h>
using namespace std;

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using isize = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using usize = size_t;
using f32 = float_t;
using f64 = double_t;

inline constexpr i32 Modulus = 1e9 + 7;

int main(void)
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);

    usize n;
    cin >> n;

    usize answer = 1;
    vector<u32> dp(n, numeric_limits<u32>::max());
    for (usize index = 0; index < n; index += 1)
    {
        u32 num;
        cin >> num;

        usize lower = lower_bound(dp.begin(), dp.end(), num) - dp.begin();
        dp[lower] = min(dp[lower], num);
        answer = max(answer, lower + 1);
    }

    cout << answer;

    return 0;
}