Submission #41975512

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#include <bits/stdc++.h>
using namespace std;
#define mp make_pair
#define pb push_back
#define int long long
#define pii pair<int, int>
#define fi first
#define se second
#define all(v) v.begin(), v.end()
#define trace(x) cout << '>' << #x << ':' << x << "\n"
#define trace2(x,y) cout<< '>' << #x << ':' << x << " | " << #y << ':' << y << "\n"
#define trace3(a,b,c) cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<"\n"
#define trace4(a,b,c,d) cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<", "<<#d<<"="<<(d)<<"\n"
template <typename T>
void print(T var){
    cout << var << ' ';
    return;
 
 
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#include <bits/stdc++.h>

using namespace std;

#define mp make_pair
#define pb push_back
#define int long long
#define pii pair<int, int>
#define fi first
#define se second
#define all(v) v.begin(), v.end()

#define trace(x) cout << '>' << #x << ':' << x << "\n"
#define trace2(x,y) cout<< '>' << #x << ':' << x << " | " << #y << ':' << y << "\n"
#define trace3(a,b,c) cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<"\n"
#define trace4(a,b,c,d) cout<<#a<<"="<<(a)<<", "<<#b<<"="<<(b)<<", "<<#c<<"="<<(c)<<", "<<#d<<"="<<(d)<<"\n"

template <typename T>
void print(T var){
    cout << var << ' ';
    return;
}

template <typename T>
void print(vector <T> var){
    for (auto x: var)
        print(x);
    cout << "\n";
    return;
}

int dx[4] = {-1, 0, 1, 0};
int dy[4] = {0, -1, 0, 1};
const int mod = 998244353;

bool prime(int x) {
    if (x==1) return true;
    for (int i = 2; i*i <= x; i++) {
        if (x%i==0) return false;
    }
    return true;
}

int f(int a, int b) {
    if (b==0) return 1;
    int res = f(a,b/2);
    res = (res*res) % mod;
    if (b&1) res = (a*res) % mod;
    return res;
}

signed main(){

    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);

    int n;
    cin >> n;

    string s;
    cin >> s;

    vector<int> dp(n+1,0);

    int ans = 0;
    for (int i = 1; i < n; i++) {
        // if (!prime(i)) continue;
        if (n%i!=0) continue;
        vector<bool> v(i,false);
        for (int j = 0; j < n; j++) {
            if (s[j]=='.') {
                int cur = j%i;
                v[cur] = true;
            }
        }
        int c = 0;
        for (int j = 0; j < i; j++) {
            if (v[j]) c++;
        }
        // trace2(i,i-c);
        dp[i] = (dp[i]+f(2,i-c)) % mod;
        for (int j = 2*i; j <= n; j+= i) {
            dp[j] -= dp[i];
            dp[j] += mod;
            dp[j] %= mod;
        }
    }    

    for (int i = 1; i < n; i++) {
        // if (!prime(i)) continue;
        if (n%i!=0) continue;
        ans = (ans+dp[i]) % mod;
        ans = (ans+mod) % mod;
    }

    cout << ans;

}

Submission Info

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