BONUS - VOI 2021 - Sqrt Decomposition

//Make CSP great again
//You're as beautiful as the day I lost you
//New year, best wishes
#include <bits/stdc++.h>
#define TASK "TESTCODE"
#define Log2(x) 31 - __builtin_clz(x)
using namespace std;
const int N = 3e5, K = 1e6, M = 1e5, block = 550;
int n, m, a[N + 1];
long long dp[K + 1], add[K + 1], luck[M + 1], f[M + 1], res = 0;
vector<int> Adj[M + 1];
struct Trie
{
    struct node
    {
        int child[26];
        node()
        {
            memset(child, -1, sizeof(child));
        }
    };
    vector<node> Tree;
    void new_node()
    {
        node tmp;
        Tree.push_back(tmp);
    }
    Trie()
    {
        new_node();
    }
    int Index(string &s)
    {
        int id = 0;
        for (char c : s)
        {
            int w = c - 'A';
            if (Tree[id].child[w] == -1)
            {
                Tree[id].child[w] = Tree.size();
                new_node();
            }
            id = Tree[id].child[w];
        }
        return id;
    }
    void Update(string &s, int u)
    {
        int id = 0;
        for (char c : s)
        {
            int w = c - 'A';
            add[id] = max(add[id], dp[u]);
            id = Tree[id].child[w];
        }
    }
} Tree;
string s[N + 1];
void read()
{
    cin >> n >> m;
    for (int i = 1; i <= n; ++ i)
    {
        cin >> s[i] >> a[i];
    }
    for (int i = 1; i <= m; ++ i)
    {
        int u, v;
        cin >> u >> v;
        Adj[u].push_back(v);
        Adj[v].push_back(u);
    }
    for (int i = 1; i <= M; ++ i)
    {
        sort(Adj[i].begin(), Adj[i].end(), [](const int &x, const int &y)
        {
            return Adj[x].size() > Adj[y].size();
        });
    }
}
long long Get(int u, long long x)
{
    if (Adj[u].size() <= block)
    {
        long long t = luck[u];
        t = max(t, x);
        for (int v : Adj[u])
        {
            if (Adj[v].size() <= block)
            {
                break;
            }
            t = max(t, f[v]);
        }
        for (int v : Adj[u])
        {
            luck[v] = max(luck[v], t + u);
        }
        return t + u;
    }
    else
    {
        long long t = luck[u];
        t = max(t, x);
        for (int v : Adj[u])
        {
            if (Adj[v].size() <= block)
            {
                break;
            }
            luck[v] = max(luck[v], t + u);
        }
        f[u] = max(f[u], t + u);
        return t + u;
    }
}
void solve()
{
    for (int i = 1; i <= n; ++ i)
    {
        int j = Tree.Index(s[i]);
        long long t = Get(a[i], add[j]);
        dp[j] = max(dp[j], t);
        res = max(res, t);
        Tree.Update(s[i], j);
        //cerr << res << '\n';
    }
    cout << res;
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    if (fopen(TASK".INP", "r"))
    {
        freopen(TASK".INP", "r", stdin);
        //freopen(TASK".out", "w", stdout);
    }
    int t = 1;
    bool typetest = false;
    if (typetest)
    {
        cin >> t;
    }
    for (int __ = 1; __ <= t; ++ __)
    {
        //cout << "Case " << __ << ": ";
        read();
        solve();
    }
}