#include<bits/stdc++.h>
using namespace std;
//#include<ext/pb_ds/assoc_container.hpp>
//#include<ext/pb_ds/tree_policy.hpp>
//
// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("Ofast")
// #pragma GCC optimize("-O3")
// #pragma GCC optimize("no-stack-protector")
// #pragma GCC optimize("fast-math")
//#define LOCAL
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cout<< *x, 0);
sim > char dud(...);
struct debug {
#ifndef LOCAL
~debug() { cout << endl; }
eni(!=) cout << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it)
*this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
#define fi first
#define f first
#define se second
#define s second
#define vi_a vector<int>a;
#define p_b push_back
////////////////////////////////???????????????CHECK THIS OUT???????????????//////////////////////////////
#define ll long long
////////////////////////////////???????????????CHECK THIS OUT???????????????//////////////////////////////
#define ld long double
#define pll pair<ll,ll>
#define pii pair<int,int>
#define m_p make_pair
#define fast_io cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(0);
#define all(x) x.begin(),x.end()
#define getfiles ifstream cin("input.txt");ofstream cout("output.txt");
#define pw(x) (1ll << x)
#define sz(x) (ll)x.size()
#define endl "\n"
#define rall(x) x.rbegin(),x.rend()
#define len(a) (ll)a.size()
#define rep(x,l,r) for(ll x=l;x<r;x++)
//using namespace __gnu_pbds;
ld eps = (ld)1 / 1e6;
const ld pi=3.14159265359;
ll inf = 1e18,mod1=1e9+7;
ll sqr(ll a) { return a * a; }
ll qb(ll a) { return a * a * a; }
ll gcd(ll a, ll b) { return !a ? b : gcd(b % a, a); }
ll binpow(ll a, ll b, ll mod) { return b ? (b % 2 ? (a * (sqr(binpow(a, b / 2, mod)) % mod)) % mod : sqr(binpow(a, b / 2, mod)) % mod) : 1; }
ll binmult(ll a, ll b, ll mod) { return b ? (b % 2 ? (2 * binmult(a, b / 2, mod) + a) % mod : (2 * binmult(a, b / 2, mod)) % mod) : 0; }
/////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
const ll R=1e4;
const ll tx[4]={0,0,-1,1};
const ll ty[4]={-1,1,0,0};
const char rev_to[4]={'E','W','N','S'};
const int N=5e2+1;
const int M=999999937;
const int pp=73;
const pii d[8]={{1,1},{1,-1},{-1,1},{-1,0},{1,0},{0,-1},{0,1},{-1,-1}};
ll h[8][N][N],p[8][N][N],st[8][N][N];
char a[N][N];
ll rl[8][N][N];
pii pos[8][N][N];
unordered_map<ll,int>mp;
int n,m,k;
signed main(){
fast_io;
cin>>n>>m>>k;
for(int i=0;i<n;i++) for(int j=0;j<m;j++) cin>>a[i][j];
for(int t=0;t<8;t++){
ll cur=1,pr=0,what=1;
for(int ps=0;ps<32;ps++){
/// calculating pod'em's
for(int i=0;i<n;i++){
for(int j=0;j<m;j++){
if(!ps){
h[t][i][j]=a[i][j]-'a'+1;
}
else{
int tf=((pw(ps-1)*d[t].f+i)%n+n)%n,ts=((pw(ps-1)*d[t].s+j)%m+m)%m;
// debug()<<imie(i)<<imie(j)<<imie(tf)<<imie(ts);
h[t][i][j]=(p[t][i][j]+1ll*p[t][tf][ts]*cur%M)%M;
}
}
}
pr=cur;
if(!ps){
cur=pp;
}
else{
cur=(pr*pr)%M;
// debug()<<imie(cur)<<imie(binpow(pp,pw(ps),M));
// assert(cur==binpow(pp,pw(ps),M));
}
/// calculating hashes
if(pw(ps) & k){
for(int i=0;i<n;i++){
for(int j=0;j<m;j++){
ll w=(pw(ps)-1)&k;
int f=((w*d[t].f+i)%n+n)%n,s=((w*d[t].s+j)%m+m)%m;
// debug()<<imie(what)<<imie(binpow(pp,w,M));
// cout.flush();
// assert(what==binpow(pp,w,M));
rl[t][i][j]=(rl[t][i][j]+h[t][f][s]*what%M)%M;
}
}
what=(what*cur)%M;
}
for(int i=0;i<n;i++){
for(int j=0;j<m;j++){
p[t][i][j]=h[t][i][j];
}
}
}
}
for(int t=0;t<8;t++){
for(int i=0;i<n;i++){
for(int j=0;j<m;j++){
mp[rl[t][i][j]]++;
// debug()<<imie(d[t])<<imie(i)<<imie(j)<<imie(rl[t][i][j]);
}
}
}
ll f=0,s=8*n*m;s*=s;
for(auto &z : mp){
f+=1ll*z.s*z.s;
}
ll g=__gcd(f,s);f/=g;s/=g;
cout<<f<<'/'<<s;
return 0;
}
///stuff you should look for :
/*
9
1 2
2 3
2 5
3 4
1 6
6 7
7 8
7 9
2
1
1
1
1
1
1
1
1
* int overflow, array bounds
* special cases (n=1?)
* do smth instead of nothing and stay organized
* read the conditions carefully
* WRITE STUFF DOWN
*/
Compilation message
osmosmjerka.cpp: In function 'int main()':
osmosmjerka.cpp:101:39: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
int tf=((pw(ps-1)*d[t].f+i)%n+n)%n,ts=((pw(ps-1)*d[t].s+j)%m+m)%m;
~~^~
osmosmjerka.cpp:56:23: note: in definition of macro 'pw'
#define pw(x) (1ll << x)
^
osmosmjerka.cpp:101:70: warning: suggest parentheses around '-' inside '<<' [-Wparentheses]
int tf=((pw(ps-1)*d[t].f+i)%n+n)%n,ts=((pw(ps-1)*d[t].s+j)%m+m)%m;
~~^~
osmosmjerka.cpp:56:23: note: in definition of macro 'pw'
#define pw(x) (1ll << x)
^
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
5 ms |
512 KB |
Output is correct |
| 2 |
Correct |
5 ms |
896 KB |
Output is correct |
| 3 |
Correct |
6 ms |
1408 KB |
Output is correct |
| 4 |
Correct |
8 ms |
2432 KB |
Output is correct |
| 5 |
Correct |
18 ms |
4352 KB |
Output is correct |
| 6 |
Correct |
76 ms |
11816 KB |
Output is correct |
| 7 |
Correct |
577 ms |
32392 KB |
Output is correct |
| 8 |
Correct |
2198 ms |
72468 KB |
Output is correct |
