Codeforces-solutions/Codeforces Round 1089 (Div. 2)/C2. A Simple GCD Problem (Hard Version).cpp

/* Problem URL: https://codeforces.com/contest/2210/problem/C2 */

#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;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

const int oo = INT32_MAX >> 1;
const ll OO = INT64_MAX >> 1;

ll p[] = {1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113};
int ps = sizeof(p) / sizeof(ll);

void pre()
{

}

#define TEST 1

void solve()
{
    int n;
    cin >> n;

    vl a(n);
    vl b(n);

    cin >> a >> b;

    vl act(n);
    V<bool> rem(n);
    act[0] = gcd(a[0], a[1]);
    if (act[0] > b[0]) {
        act[0] = a[0];
    }

    if (act[0] != a[0]) {
        rem[0] = true;
    }
    
    act[n - 1] = gcd(a[n - 1], a[n - 2]);
    if (act[n - 1] > b[n - 1]) {
        act[n - 1] = a[n - 1];
    }

    if (act[n - 1] != a[n - 1]) {
        rem[n - 1] = true;
    }

    nrep(i, 1, n - 1) {
        act[i] = lcm(gcd(a[i], a[i - 1]), gcd(a[i], a[i + 1]));
        if (act[i] > b[i]) {
            act[i] = a[i];
            continue;
        }

        if (act[i] != a[i]) {
            rem[i] = true;
        }
    }

    vvl dp(n, vl(ps, -OO));
    dp[0][0] = rem[0];
    if (!rem[0]) {
        rep(i, ps) {
            ll cur = p[i] * act[0];
            if (cur > b[0]) {
                break;
            }

            dp[0][i] = (cur != a[0]);
        }
    }

    nrep(i, 1, n) {
        ll bf = act[i - 1] / gcd(act[i - 1], act[i]);
        ll nw = act[i] / gcd(act[i - 1], act[i]);

        if (rem[i]) {
            dp[i][0] = dp[i - 1][0] + 1;
            nrep(k, 1, ps) {
                if (nw % p[k] != 0) {
                    rmax(dp[i][0], dp[i - 1][k] + 1);
                }
            }
            continue;
        }

        dp[i][0] = dp[i - 1][0];

        nrep(k, 1, ps) {
            if (nw % p[k] == 0) {
                continue;
            }

            rmax(dp[i][0], dp[i - 1][k]);
        }

        nrep(j, 1, ps) {
            if (act[i] * p[j] > b[i]) {
                break;
            }
            if (bf % p[j] == 0) {
                continue;
            }

            rmax(dp[i][j], dp[i - 1][0] + (act[i] * p[j] != a[i]));
            nrep(k, 1, ps) {
                if (j == k || nw % p[k] == 0) {
                    continue;
                }
                
                rmax(dp[i][j], dp[i - 1][k] + (act[i] * p[j] != a[i]));
            }
        }
    }

    cout << max(*max_element(all(dp[n - 1])), 0LL) << '\n';
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    pre();

    int t;
    (TEST && cin >> t) || (t = 1);
    while (t--) {
        solve();
    }
}