#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;
using namespace chrono;
// mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());
/*
template <class T> using ordered_set = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>;
*/
//***************** CONSTANTS *****************
const int MXN = 100001;
//***************** GLOBAL VARIABLES *****************
int N, M, K;
vector<int> g[MXN];
int a[MXN];
int64_t dp[MXN][32];
//***************** AUXILIARY STRUCTS *****************
//***************** MAIN BODY *****************
void solve(){
cin >> N >> M >> K;
for(int i = 1; i <= N; i++)
cin >> a[i];
for(int i = 0; i < M; i++){
int u, v;
cin >> u >> v;
g[u].push_back(v);
g[v].push_back(u);
}
int64_t ans = 0;
for(int mask = 1; mask < (1 << K); mask++){
for(int u = 1; u <= N; u++){
if(mask >> a[i] & 1 ^ 1)
continue;
if(__builtin_popcount(mask) == 1) dp[u][mask]++;
for(int v : g[u])
if(a[u] != a[v])
dp[u][mask] += dp[v][mask ^ (1 << a[i])];
ans += dp[u][mask];
}
}
cout << ans - N << '\n';
}
//***************** *****************
int32_t main(){
ios_base::sync_with_stdio(NULL);
cin.tie(NULL);
#ifdef LOCAL
auto begin = high_resolution_clock::now();
#endif
int tc = 1;
// cin >> tc;
for (int t = 0; t < tc; t++)
solve();
#ifdef LOCAL
auto end = high_resolution_clock::now();
cout << fixed << setprecision(4);
cout << "Execution Time: " << duration_cast<duration<double>>(end - begin).count() << "seconds" << endl;
#endif
return 0;
}
/*
If code gives a WA, check for the following :
1. I/O format
2. Are you clearing all global variables in between tests if multitests are a thing
3. Can you definitively prove the logic
*/
Compilation message
paths.cpp: In function 'void solve()':
paths.cpp:51:17: error: 'i' was not declared in this scope
51 | if(mask >> a[i] & 1 ^ 1)
| ^
paths.cpp:56:42: error: 'i' was not declared in this scope
56 | dp[u][mask] += dp[v][mask ^ (1 << a[i])];
| ^
