#include "validation.h"
#include <vector>
#include <set>

// In this file, you should validate the grammar of your input files.
// Any additional constraints mentioned in the problem statement should also be checked here.

// Please use the Validator class from the header for verifying the grammar.
// This automatically exits with code 43 (WA) when input parsing fails,
// and exits with code 42 when reading input and all tests succeeded.
// Please use v.WA("some ", "error ", "here ") to exit with code 43 manually.

// When your program crashes unexpectedly, or something weird is going on,
// please write some info to stderr and return anything different from 42 and 43.

using vi = std::vector<int>;
struct UnionFind {
	vi par, rank, size; int c;
	UnionFind(int n) : par(n), rank(n,0), size(n,1), c(n) {
		for (int i = 0; i < n; ++i) par[i] = i;
	}

	int find(int i) { return (par[i] == i ? i : (par[i] = find(par[i]))); }
	bool same(int i, int j) { return find(i) == find(j); }
	int get_size(int i) { return size[find(i)]; }
	int count() { return c; }

	void merge(int i, int j) {
		if ((i = find(i)) == (j = find(j))) return;
		c--;
		if (rank[i] > rank[j]) swap(i, j);
		par[i] = j; size[j] += size[i];
		if (rank[i] == rank[j]) rank[j]++;
	}
};

// TODO match these with the problem statement.
constexpr int MAXN = 1e5;
constexpr int MAXM = 2e5;
constexpr int MAXS = 10;
constexpr int MAXP = 1e9;
constexpr int MAXW = 1e9;
constexpr int MAXC = 1e9;

int main(int argc, char **argv) {
	InputValidator v;

	int n = v.read_int(1, MAXN);
		v.space();
	int m = v.read_int(0, MAXM);
		v.space();
	int s = v.read_int(1, MAXS);
		v.newline();

	long long total_population = 0LL;
	for (int i = 0; i < n; ++i) {
		int pi = v.read_int(0, MAXP);
		total_population += (long long)pi;
		if (i + 1 < n)
			v.space();
		else
			v.newline();
	}

	UnionFind uf(n);
	std::set<std::pair<int, int>> st;
	for (int i = 0; i < m; ++i) {
		int u1 = v.read_int(1, n);
			v.space();
		int u2 = v.read_int(1, n);
			v.space();
		int w = v.read_int(1, MAXW);
			v.newline();

		u1 -= 1, u2 -= 1;
		if (u1 > u2) swap(u1, u2);

		v.assert(u1 != u2, "Self edge on ", u1+1, " at position ", i, ".");
		v.assert(st.find({u1, u2}) == st.end(), "Double edge from ", u1,
			" to ", u2,  " with second at ", i, ".");
		st.insert({u1, u2});
		uf.merge(u1, u2);
	}

	v.assert(uf.count() == 1, "Graph must be connected.");

	long long total_shelter = 0;
	std::set<int> ss;
	for (int i = 0; i < s; ++i) {
		int si = v.read_int(1, n);
			v.space();
		int ci = v.read_int(1, MAXC);
			v.newline();

		v.assert(ss.find(si) == ss.end(), "Duplicate shelter ", si, ".");
		total_shelter += ci;
	}

	v.assert(total_shelter >= total_population, "Population size cannot be ",
			"larger than shelter size.");
}