#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;
#define int long long
#define fi first
#define se second
#define pb push_back
mt19937 rng((int)chrono::steady_clock::now().time_since_epoch().count());
int hashp = uniform_int_distribution<int>(257, 1e9)(rng);
int hashm1 = 1e9+7;
int be(int cur, int exp){
if(exp == 0) return 1;
int res = 1;
while(exp){
if(exp % 2 == 0){
exp >>= 1;
cur *= cur;
cur %= hashm1;
} else{
exp--;
res *= cur;
res %= hashm1;
}
}
return res;
}
long long gs(long long r, long long n) {
if (n == 0) return 0;
if (n == 1) return 1;
if (n % 2 == 0) {
long long half_sum = gs(r, n / 2);
long long multiplier = (1 + be(r, n / 2)) % hashm1;
return (half_sum * multiplier) % hashm1;
} else {
return (1 + r * gs(r, n - 1)) % hashm1;
}
}
void solve(){
int m, n, k;
cin >> m >> n >> k;
vector<string> a(m);
for(int i = 0; i < m; i++) cin >> a[i];
map<int, int> mp;
int max_len = m * n + 5;
vector<int> p(max_len, 1);
for(int i = 1; i < max_len; i++){
p[i] = (p[i-1]*hashp) % hashm1;
}
int dx[] = {-1, 1, 0, 0, -1, -1, 1, 1};
int dy[] = {0, 0, -1, 1, -1, 1, -1, 1};
for(int d = 0; d < 8; d++) {
vector<vector<bool>> vis(m, vector<bool>(n, false));
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
if(vis[i][j]) continue;
vector<int> line;
int r = i, c = j;
while(!vis[r][c]){
vis[r][c] = true;
line.pb(a[r][c]);
r = (r + dx[d] + m) % m;
c = (c + dy[d] + n) % n;
}
int sz = line.size();
vector<int> end(sz, 0);
end[0] = line[0];
for(int x = 1; x < sz; x++){
end[x] = (end[x-1] * hashp + line[x]) % hashm1;
}
for(int x = 0; x < sz; x++){
int total_reps = k / sz;
int rem = k % sz;
int prev = (x == 0) ? 0 : end[x-1];
int part1 = (end[sz-1] - (prev * p[sz-x]) % hashm1 + hashm1) % hashm1;
int rot_hash = part1;
if(x > 0) {
rot_hash = (rot_hash * p[x] + end[x-1]) % hashm1;
}
int term1 = (rot_hash * gs(p[sz], total_reps)) % hashm1;
int final_hash = (term1 * p[rem]) % hashm1;
if (rem > 0) {
int rem_hash;
if(x + rem <= sz) {
int prev_rem = (x == 0) ? 0 : end[x-1];
rem_hash = (end[x+rem-1] - (prev_rem * p[rem]) % hashm1 + hashm1) % hashm1;
} else {
int first_chunk_len = sz - x;
int second_chunk_len = rem - first_chunk_len;
int prev_wrap = (x == 0) ? 0 : end[x-1];
int h1 = (end[sz-1] - (prev_wrap * p[first_chunk_len]) % hashm1 + hashm1) % hashm1;
int h2 = end[second_chunk_len-1];
rem_hash = (h1 * p[second_chunk_len] + h2) % hashm1;
}
final_hash = (final_hash + rem_hash) % hashm1;
}
mp[final_hash]++;
}
}
}
}
__int128 num = 0;
for(auto &pi : mp){
num += (__int128)pi.second * pi.second;
}
__int128 total = (__int128)m * n * 8;
__int128 denom = total * total;
__int128 cd = std::gcd((long long)num, (long long)denom);
num /= cd;
denom /= cd;
cout << (long long)num << "/" << (long long)denom;
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
