Problem: Misha has a tree with characters written on the vertices. He can choose two vertices s and t of this tree and write down characters of vertices lying on a path from s to t. We'll say that such string corresponds to pair (s, t).

Misha has m queries of type: you are given 4 vertices a, b, c, d; you need to find the largest common prefix of the strings that correspond to pairs (a, b) and (c, d). Your task is to help him.

Input

The first line contains integer n (1 ≤ n ≤ 300 000) — the number of vertices in the tree.

Next follows a line consisting of n small English letters. The i-th character of the string corresponds to the character written on the i-th vertex. 

Next n - 1 lines contain information about edges. An edge is defined by a pair of integers u, v (1 ≤ u, v ≤ n, u ≠ v), separated by spaces.

The next line contains integer m (1 ≤ m ≤ 1 000 000) — the number of queries.

Next m lines contain information about queries. A query is defined by four integers a, b, c, d (1 ≤ a, b, c, d ≤ n), separated by spaces.

Output

For each query print the length of the largest common prefix on a separate line.

Examples

Input

6
bbbabb
2 1
3 2
4 3
5 2
6 5
6
2 5 3 1
1 5 2 3
5 6 5 6
6 3 4 1
6 2 3 4
2 2 4 5


Output

2
2
2
0
1
0

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct Query {
  int a, b, c, d, l1, l2;
};
const int MOD = 1000000123;
const int BASE = 29;
const int INV = 758620783;
int powB[300013], powI[300013];
int n, m;
char s[300013];
vector<int> adj[300013];
int up[19][300013];
int h[300013];
inline int go(int a, int d) {
  int i = 0;
  while (d) {
    if (d & 1) a = up[i][a];
    d >>= 1, i += 1;
  }
  return a;
}
inline int lca(int a, int b) {
  if (h[a] > h[b]) swap(a, b);
  b = go(b, h[b] - h[a]);
  if (a == b) return a;
  for (int i = 18; i >= 0; i--)
    if (up[i][a] != up[i][b]) a = up[i][a], b = up[i][b];
  return up[0][a];
}
vector<int> topo;
int hash_[300013], hsah[300013];
inline void dfs(int x, int p = 0) {
  up[0][x] = p;
  h[x] = h[p] + 1;
  topo.push_back(x);
  hash_[x] = ((long long)(s[x] - 'a' + 1) * powB[h[x]] + hash_[p]) % MOD;
  hsah[x] = ((long long)hsah[p] * BASE + (s[x] - 'a' + 1)) % MOD;
  for (int i : adj[x])
    if (i != p) dfs(i, x);
}
inline void build() {
  powB[0] = 1;
  for (int i = 1; i < 300013; i++)
    powB[i] = ((long long)BASE * powB[i - 1]) % MOD;
  powI[0] = 1;
  for (int i = 1; i < 300013; i++)
    powI[i] = ((long long)INV * powI[i - 1]) % MOD;
  h[0] = -1;
  dfs(1);
  for (int i = 1; i < 19; i++)
    for (int j = 1; j <= n; j++) {
      up[i][j] = up[i - 1][up[i - 1][j]];
    }
}
inline int get(int a, int l, int b, int len) {
  if (len <= h[a] - h[l] + 1) {
    b = up[0][b];
    return ((long long)(hash_[a] - hash_[b] + MOD) * powI[h[b] + 1]) % MOD;
  } else {
    int p = l;
    l = up[0][l];
    int fac = (h[b] - 2 * h[l] - 2 >= 0) ? powB[h[b] - 2 * h[l] - 2]
                                         : powI[2 * h[l] + 2 - h[b]];
    int res = ((long long)(hash_[a] - hash_[p]) * fac + hsah[b] -
               (long long)hsah[l] * powB[h[b] - h[l]]) %
              MOD;
    if (res < 0) res += MOD;
    return res;
  }
}
Query q[1000013];
pair<int, int> bound[1000013];
int len[1000013][2];
int res[2 * 1000013];
int last[300013];
vector<pair<int, int> > need[300013];
inline void solve() {
  for (int i = 0; i < m; i++) {
    q[i].l1 = lca(q[i].a, q[i].b);
    q[i].l2 = lca(q[i].c, q[i].d);
    len[i][0] = h[q[i].a] + h[q[i].b] - 2 * h[q[i].l1] + 1;
    len[i][1] = h[q[i].c] + h[q[i].d] - 2 * h[q[i].l2] + 1;
    bound[i] = make_pair(0, min(len[i][0], len[i][1]) + 1);
  }
  for (int r = 0; r < 19; r++) {
    for (int i = 1; i <= n; i++) need[i].clear();
    for (int i = 0; i < m; i++)
      if (bound[i].second - bound[i].first > 1) {
        int mid = (bound[i].first + bound[i].second) / 2;
        if (mid <= h[q[i].a] - h[q[i].l1] + 1)
          need[q[i].a].push_back(make_pair(mid - 1, i * 2));
        else
          need[q[i].b].push_back(make_pair(len[i][0] - mid, i * 2));
        if (mid <= h[q[i].c] - h[q[i].l2] + 1)
          need[q[i].c].push_back(make_pair(mid - 1, i * 2 + 1));
        else
          need[q[i].d].push_back(make_pair(len[i][1] - mid, i * 2 + 1));
      }
    for (int i : topo) {
      last[h[i]] = i;
      for (auto j : need[i]) {
        res[j.second] = last[h[i] - j.first];
      }
    }
    for (int i = 0; i < m; i++)
      if (bound[i].second - bound[i].first > 1) {
        int mid = (bound[i].first + bound[i].second) / 2;
        int one = get(q[i].a, q[i].l1, res[2 * i], mid);
        int two = get(q[i].c, q[i].l2, res[2 * i + 1], mid);
        if (one == two)
          bound[i].first = mid;
        else
          bound[i].second = mid;
      }
  }
}
inline int readint() {
  char c;
  while ((c = getchar()) < '0') continue;
  int ress = c - '0';
  while ((c = getchar()) >= '0') ress = ress * 10 + c - '0';
  return ress;
}
int main() {
  n = readint();
  for (int i = 1; i <= n; i++) s[i] = getchar();
  for (int i = 1; i < n; i++) {
    int u = readint(), v = readint();
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  build();
  m = readint();
  for (int i = 0; i < m; i++) {
    q[i].a = readint(), q[i].b = readint(), q[i].c = readint(),
    q[i].d = readint();
  }
  solve();
  for (int i = 0; i < m; i++) printf("%d\n", bound[i].first);
  return 0;
}