最后一个点TLE，求教大佬们Orz!

#include <iostream>
#include <vector>
using namespace std;

const int MAX_N = 1e8 + 10;
bool cnt[MAX_N];

int main() {
    int N;
    scanf("%d", &N);
    vector<int> primes;
    for (int i = 2; i <= N; i++) {
        if (cnt[i] == false)
            primes.push_back(i);
        for (int j : primes) {
            if (i * j > N)
                break;
            cnt[i * j] = true;
            if (i % j == 0)
                break;
        }
    }
    printf("%d\n", primes.size());
    return 0;
}