Problem: Given the string S and m queries. The i-th query is given by the two strings xi and yi.

For each query, answer the longest substring of the string S, starting with xi and ending with yi.

For the string S, | S | represents the length of S. Also, the fact that the character string T is a substring of the character string S means that a certain integer i exists and Tj = Si + j is satisfied for 1 ≤ j ≤ | T |. Where Tj represents the jth character of T.

Constraints

* 1 ≤ | S | ≤ 2 x 105
* 1 ≤ m ≤ 105
* 1 ≤ | xi |, | yi |
* $ \ sum ^ m_ {i = 1} $ (| xi | + | yi |) ≤ 2 x 105
* S and xi, yi consist only of half-width lowercase letters.

Input

The input is given in the following format.


S
m
x1 y1
x2 y2
::
xm ym


* The character string S is given on the first line.
* The number of queries m is given in the second line.
* Of the m lines from the 3rd line, the i-th query string xi, yi is given on the i-th line, separated by spaces.

Output

Answer the maximum substring length in the following format.


len1
len2
::
lenm


Output the longest substring length leni that satisfies the condition for the i-th query on the i-th line of the m lines from the first line. If there is no such substring, output 0.

Examples

Input

abracadabra
5
ab a
a a
b c
ac ca
z z


Output

11
11
4
3
0


Input

howistheprogress
4
ist prog
s ss
how is
the progress


Output

9
12
5
11


Input

icpcsummertraining
9
mm m
icpc summer
train ing
summer mm
i c
i i
g g
train i
summer er


Output

2
10
8
0
4
16
1
6
6

Solution (in CPP):

Solution:
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

struct suffix_array {
  int n;
  vector<int> sa;

  suffix_array(string const& S) {
    vector<int> rank, temp;
    n = S.size();
    rank.resize(n + 1);
    temp.resize(n + 1);
    sa.resize(n + 1);
    for(int i=0; i<=n; i++) {
      sa[i] = i;
      rank[i] = i < n ? S[i] : -1;
    }

    for(int k=1; k<=n; k*=2) {

      const auto compare = [&](int i, int j) {
        if(rank[i] != rank[j]) return rank[i] < rank[j];
        int ri = i + k <= n ? rank[i + k] : -1;
        int rj = j + k <= n ? rank[j + k] : -1;
        return ri < rj;
      };

      sort(sa.begin(), sa.end(), compare);
      temp[sa[0]] = 0;
      for(int i=1; i<=n; i++) {
        temp[sa[i]] = temp[sa[i-1]] + (compare(sa[i-1], sa[i]) ? 1 : 0);
      }
      for(int i=0; i<=n; i++) {
        rank[i] = temp[i];
      }
    }
  }

  int operator[](int i) { return sa.at(i); }

  static int const npos = -1;

  int lower_bound(string const& S, string const& T) {
    int l = 0, r = n;
    int tsize = T.size();
    while(l + 1 < r) {
      int m = (l + r) / 2;
      (S.compare(sa[m], tsize, T) < 0 ? l : r) = m;
    }
    return S.compare(sa[r], tsize, T) == 0 ? r : npos;
  }

  int upper_bound(string const& S, string const& T) {
    int l = 1, r = n + 1;
    int tsize = T.size();
    while(l + 1 < r) {
      int m = (l + r) / 2;
      (S.compare(sa[m], tsize, T) <= 0 ? l : r) = m;
    }
    return S.compare(sa[l], tsize, T) == 0 ? r : npos;
  }
};

enum query_type { min_query, max_query };

template<class T> struct segtree {
  int N;
  vector<T> dat, sum;
  function<T(T, T)> func;
  T ngvalue;

  void init(int n, function<T(T, T)> const& f, T ng) {
    N = 1;
    while(N < n) N <<= 1;
    dat.assign(2 * N - 1, 0);
    sum.assign(2 * N - 1, 0);
    func = f;
    ngvalue = ng;
  }

  segtree(int n, query_type qtype) {
    if(qtype == min_query) {
      init(n, [](T a, T b){return min(a, b);}, numeric_limits<T>::max());
    }
    else if(qtype == max_query) {
      init(n, [](T a, T b){return max(a, b);}, numeric_limits<T>::min());
    }
    else {
      runtime_error("no matching query type");
    }
  }

  void update(int i, T x) {
    add(i, i + 1, x);
  }

  void add(int a, int b, T x) {
    add(a, b, x, 0, 0, N);
  }

  T add(int a, int b, T x, int k, int l, int r) {
    if(b <= l || r <= a) return dat[k];
    if(a <= l && r <= b) {
      sum[k] += x;
      return dat[k] += x;
    }
    int m = (l + r) / 2;
    return dat[k] = func(add(a, b, x, 2 * k + 1, l, m), add(a, b, x, 2 * k + 2, m, r)) + sum[k];
  }

  T operator()(int a, int b) {
    return query(a, b, 0, 0, N);
  }

  T query(int a, int b, int k, int l, int r) {
    if(b <= l || r <= a) return ngvalue;
    if(a <= l && r <= b) return dat[k];
    int m = (l + r) / 2;
    return func(query(a, b, 2 * k + 1, l, m), query(a, b, 2 * k + 2, m, r)) + sum[k];
  }
};

char buf[(int)2e5 + 10];

void solve(segtree<ll>& min_query, segtree<ll>& max_query, suffix_array& sa, string const& S) {
  scanf("%s", buf); string a = buf;
  scanf("%s", buf); string b = buf;
  int a_size = a.size();
  int b_size = b.size();

  int a_lb = sa.lower_bound(S, a);
  if(a_lb == suffix_array::npos) { puts("0"); return; }
  int a_ub = sa.upper_bound(S, a);

  int b_lb = sa.lower_bound(S, b);
  if(b_lb == suffix_array::npos) { puts("0"); return; }
  int b_ub = sa.upper_bound(S, b);
  
  int l = min_query(a_lb, a_ub);
  int r = max_query(b_lb, b_ub);
  
  if(l > r) { puts("0"); return; }
  if(r + b_size < l + a_size) { puts("0"); return; }
  printf("%d\n", r - l + b_size);
}

int main() {

  scanf("%s", buf);
  string S = buf;

  suffix_array sa(S);

  int N = S.size() + 1;
  segtree<ll> min_query(N, query_type::min_query);
  segtree<ll> max_query(N, query_type::max_query);
  for(int i=0; i<N; i++) {
    min_query.update(i, sa[i]);
    max_query.update(i, sa[i]);
  }

  int M; cin >> M;
  while(M--) {
    solve(min_query, max_query, sa, S);
  }
  return 0;
}