#include <bits/stdc++.h>
using namespace std;
#define int long long
#define pb push_back
const int MOD1 = 1e9 + 7;
const int MOD2 = 1e9 + 9;
mt19937 rng((int)chrono::steady_clock::now().time_since_epoch().count());
int P1 = uniform_int_distribution<int>(257, 1e9)(rng);
int P2 = uniform_int_distribution<int>(257, 1e9)(rng);
int power(int base, int exp, int mod) {
int res = 1;
base %= mod;
while (exp > 0) {
if (exp % 2 == 1) res = (res * base) % mod;
base = (base * base) % mod;
exp /= 2;
}
return res;
}
int gs(int r, int n, int mod) {
if (n == 0) return 0;
if (n == 1) return 1;
if (n % 2 == 0) {
int half = gs(r, n / 2, mod);
int mul = (1 + power(r, n / 2, mod)) % mod;
return (half * mul) % mod;
} else {
return (1 + r * gs(r, n - 1, mod)) % mod;
}
}
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<pair<int, int>, int> mp;
int max_len = m * n + 5;
vector<int> p1(max_len, 1), p2(max_len, 1);
for (int i = 1; i < max_len; i++) {
p1[i] = (p1[i - 1] * P1) % MOD1;
p2[i] = (p2[i - 1] * P2) % MOD2;
}
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> h1(sz, 0), h2(sz, 0);
h1[0] = line[0];
h2[0] = line[0];
for (int x = 1; x < sz; x++) {
h1[x] = (h1[x - 1] * P1 + line[x]) % MOD1;
h2[x] = (h2[x - 1] * P2 + line[x]) % MOD2;
}
for (int x = 0; x < sz; x++) {
int total_reps = k / sz;
int rem = k % sz;
int prev1 = (x == 0) ? 0 : h1[x - 1];
int rot1 = (h1[sz - 1] - (prev1 * p1[sz - x]) % MOD1 + MOD1) % MOD1;
if (x > 0) rot1 = (rot1 * p1[x] + h1[x - 1]) % MOD1;
int term1_1 = (rot1 * gs(p1[sz], total_reps, MOD1)) % MOD1;
int final1 = (term1_1 * p1[rem]) % MOD1;
int prev2 = (x == 0) ? 0 : h2[x - 1];
int rot2 = (h2[sz - 1] - (prev2 * p2[sz - x]) % MOD2 + MOD2) % MOD2;
if (x > 0) rot2 = (rot2 * p2[x] + h2[x - 1]) % MOD2;
int term1_2 = (rot2 * gs(p2[sz], total_reps, MOD2)) % MOD2;
int final2 = (term1_2 * p2[rem]) % MOD2;
if (rem > 0) {
int rem1, rem2;
if (x + rem <= sz) {
int p_rem1 = (x == 0) ? 0 : h1[x - 1];
rem1 = (h1[x + rem - 1] - (p_rem1 * p1[rem]) % MOD1 + MOD1) % MOD1;
int p_rem2 = (x == 0) ? 0 : h2[x - 1];
rem2 = (h2[x + rem - 1] - (p_rem2 * p2[rem]) % MOD2 + MOD2) % MOD2;
} else {
int len1 = sz - x;
int len2 = rem - len1;
int p_wrap1 = (x == 0) ? 0 : h1[x - 1];
int chunk1_1 = (h1[sz - 1] - (p_wrap1 * p1[len1]) % MOD1 + MOD1) % MOD1;
int chunk1_2 = h1[len2 - 1];
rem1 = (chunk1_1 * p1[len2] + chunk1_2) % MOD1;
int p_wrap2 = (x == 0) ? 0 : h2[x - 1];
int chunk2_1 = (h2[sz - 1] - (p_wrap2 * p2[len1]) % MOD2 + MOD2) % MOD2;
int chunk2_2 = h2[len2 - 1];
rem2 = (chunk2_1 * p2[len2] + chunk2_2) % MOD2;
}
final1 = (final1 + rem1) % MOD1;
final2 = (final2 + rem2) % MOD2;
}
mp[{final1, final2}]++;
}
}
}
}
__int128 num = 0;
for (auto const& [key, val] : mp) {
num += (__int128)val * val;
}
__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 << "\n";
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
solve();
return 0;
}
