This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
typedef int ll;
typedef long double ld;
#define pb push_back
#define pf push_front
#define fi first
#define se second
const ll mod = 1e9+11, mxn = 5e4+7;
string s;
ll sz[mxn], n, pw[mxn], up[mxn], dn[mxn], d[mxn];
bool del[mxn], ck;
vector<vector<ll>> g(mxn);
struct h_f {ll operator() (const pair<ll,ll>& x) const {return x.fi^x.se;}};
unordered_set<pair<ll,ll>,h_f> mp;
void dfs_sz(ll u, ll v) {sz[u] = 1; for (ll i : g[u]) {if (i != v && !del[i]) {dfs_sz(i,u); sz[u] += sz[i];}}}
ll dfs_ctr(ll u, ll v, ll szx) {for (ll i : g[u]) {if (i != v && !del[i] && sz[i] > szx/2) {return dfs_ctr(i,u,szx);}} return u;}
ll vv(ll x) {return s[x]-'a'+1;}
void cal(ll u, ll v)
{
for (ll i : g[u])
{
if (i != v && !del[i])
{
d[i] = d[u]+1;
up[i] = (up[u]+(long long)vv(i)*pw[d[i]])%mod;
dn[i] = ((long long)dn[u]*31+vv(i))%mod;
cal(i,u);
}
}
}
void upd_ans(ll u, ll v, ll cr, ll root)
{
if (ck) return;
if (d[u] == cr) if (((long long)up[u]+vv(root))%mod == dn[u])
{
// cerr << "SINGLE ROAD: " << u << '\n';
ck = 1;
}
// cerr << "CHECKED VALUE: " << u << ' ' << d[u] << ' ' << ((up[u]*pw[cr-d[u]]-dn[u])%mod+mod)%mod << '\n';
if (mp.count({d[u],(((long long)up[u]*pw[cr-d[u]]-dn[u])%mod+mod)%mod})) ck = 1;
if (ck) return;
for (ll i : g[u]) {if (i != v && !del[i]) {upd_ans(i, u, cr, root);}}
}
void add(ll u, ll v, ll cr)
{
if (ck) return;
if (d[u] < cr)
{
// cerr << "ADDED VALUE: " << u << ' ' << cr-d[u] << ' ' << ((up[u]*pw[cr-d[u]]-dn[u])%mod+mod)%mod << '\n';
mp.insert({cr-d[u],(((long long)up[u]*pw[cr-d[u]]-dn[u])%mod+mod)%mod});
}
for (ll i : g[u]) {if (i != v && !del[i]) {add(i, u, cr);}}
}
void upd(ll u, ll cr)
{
// cerr << "CENTROID: " << u << '\n';
if (ck) return;
d[u] = up[u] = 0; dn[u] = vv(u); cal(u,u); mp.clear();
for (ll i : g[u])
{
if (!del[i])
{
upd_ans(i,u,cr,u);
add(i,u,cr);
}
}
mp.clear();
}
void solve(ll u, ll cr)
{
dfs_sz(u,u); ll n_root = dfs_ctr(u,u,sz[u]);
upd(n_root, cr); del[n_root] = 1;
if (ck) return;
for (ll i : g[n_root]) {if (!del[i]) solve(i, cr);}
}
signed main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// freopen("test.inp","r",stdin); freopen("test.out","w",stdout); freopen("test.err","w",stderr);
cin >> n >> s; s = '#' + s; pw[0] = 1;
for (ll i = 1; i <= n; i++) pw[i] = ((long long)pw[i-1]*31)%mod;
for (ll i = 1; i < n; i++)
{
ll a, b; cin >> a >> b;
g[a].pb(b); g[b].pb(a);
}
ll l = 0, r = n; ll ans = 0;
while (r >= l)
{
ll m = (r+l)>>1;
ck = 0; mp.clear();
for (ll i = 1; i <= n; i++) del[i] = 0;
// cerr << "CURRENT LENGTH: " << m << '\n' << '\n';
solve(1,m);
// cerr << '\n';
if (ck) {ans = m; l = m+1;}
else
{
ck = 0; mp.clear();
for (ll i = 1; i <= n; i++) del[i] = 0;
// cerr << "CURRENT LENGTH: " << m+1 << '\n' << '\n';
solve(1,m+1);
// cerr << '\n';
if (ck) {ans = m; l = m+1;}
else r = m-1;
}
}
ck = 0; mp.clear();
for (ll i = 1; i <= n; i++) del[i] = 0;
solve(1,ans+1);
if (ck) cout << ans+2;
else cout << ans+1;
}
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