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| #include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <vector>
#define maxn 200010
#define maxm 20
#define INF 1000000000
#define ll long long
#define pb push_back
using namespace std;
int n, m;
char s[maxn]; int w[maxn];
struct Edge {
int to, next, w;
} e[maxn * 2]; int c1, head[maxn];
inline void add_edge(int u, int v) {
e[c1].to = v; e[c1].next = head[u]; head[u] = c1++;
}
bool vis[maxn];
struct Calc_sz {
int sz[maxn], f[maxn], sum, rt;
void init() { f[rt = 0] = INF; }
void dfs_sz(int u, int fa) {
sz[u] = 1;
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (v == fa || vis[v]) continue;
dfs_sz(v, u); sz[u] += sz[v];
}
}
void dfs(int u, int fa) {
f[u] = 0;
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (v == fa || vis[v]) continue;
dfs(v, u); f[u] = max(f[u], sz[v]);
} f[u] = max(f[u], sum - sz[u]);
if (f[u] < f[rt]) rt = u;
}
inline int get_rt(int u) {
rt = 0; dfs_sz(u, 0); sum = sz[u]; dfs(u, 0); return rt;
}
} _;
int a[maxn], c2, dis[1 << maxm];
void Dfs(int u, int fa, int S) {
a[++c2] = S;
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (v == fa || vis[v]) continue;
Dfs(v, u, S ^ w[v]);
}
}
ll ans[maxn];
ll dfs(int u, int fa, int S) {
ll sum = dis[S];
for (int i = 0; i < 20; ++i) sum += dis[S ^ 1 << i];
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (v == fa || vis[v]) continue;
sum += dfs(v, u, S ^ w[v]);
} ans[u] += sum;
return sum;
}
vector<int> I;
ll calc(int u, int fa, bool F) {
c2 = 0; Dfs(u, 0, w[u]); ll sum = 0;
if (F) {
for (int i = 1; i <= c2; ++i) ++dis[a[i]], I.pb(a[i]);
return 0;
}
for (int i = 1; i <= c2; ++i) --dis[a[i]];
sum = dfs(u, 0, w[u] ^ w[fa]);
for (int i = 1; i <= c2; ++i) ++dis[a[i]];
return sum;
}
void divide(int u) {
vis[u] = 1; dis[0] = 1;
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (vis[v]) continue;
calc(v, u, 1);
} ll sum = dis[w[u]];
for (int i = 0; i < 20; ++i) sum += dis[w[u] ^ 1 << i];
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (vis[v]) continue;
sum += calc(v, u, 0);
} ans[u] += sum / 2; for (auto u : I) dis[u] = 0; I.clear();
for (int i = head[u]; ~i; i = e[i].next) {
int v = e[i].to; if (vis[v]) continue;
divide(_.get_rt(v));
}
}
int main() { memset(head, -1, sizeof head);
cin >> n;
for (int i = 1; i < n; ++i) {
int x, y; scanf("%d%d", &x, &y);
add_edge(x, y); add_edge(y, x);
} scanf("%s", s + 1);
for (int i = 1; i <= n; ++i) w[i] = 1 << s[i] - 'a';
_.init(); divide(_.get_rt(1));
for (int i = 1; i <= n; ++i) printf("%I64d ", ans[i] + 1);
return 0;
}
|