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>

template <::std::size_t maximum, ::std::size_t max_digit,
	class RandomAccessIterator, class F>
	void LSD_RadixSort(RandomAccessIterator first, RandomAccessIterator last,
		const F &get_digit) {
	using value_type =
		typename ::std::iterator_traits<RandomAccessIterator>::value_type;
	using size_type = ::std::size_t;

	const ::std::vector<value_type> cpy(first, last);
	const size_type size = cpy.size();
	::std::array<size_type, maximum + 2> count;
	::std::vector<size_type> cur(size), tmp(size);

	::std::iota(cur.begin(), cur.end(), 0);

	for (size_type digit = 0; digit < max_digit; ++digit) {
		::std::fill(count.begin(), count.end(), 0);
		for (const auto i : cur) {
			++count[get_digit(cpy[i], digit) + 1];
		}

		for (size_type i = 1; i < maximum; ++i) {
			count[i + 1] += count[i];
		}

		for (const auto i : cur) {
			tmp[count[get_digit(cpy[i], digit)]++] = i;
		}

		::std::swap(cur, tmp);
	}

	for (size_type i = 0; i < size; ++i) {
		*(first + i) = cpy[cur[i]];
	}
}

template<typename T = ::std::string>
class SuffixArray {
private:
	::std::size_t size;
	T s;
	::std::vector<int> rank, sa, _lcp;
	::std::vector<::std::vector<int>> table; // sparse table to calculate _lcp
	::std::vector<int> log2;

	int k; // for doubling

public:
	SuffixArray() {}
	SuffixArray(T s) :s(s), size(s.size()), sa(size + 1), rank(size + 1), _lcp(size + 1, -1) {
		log2.resize(size + 1);
		for (int i = 2;i < size + 1;i++)
			log2[i] = log2[i >> 1] + 1;
	}

	::std::vector<int> build_sa() {
		::std::vector<int> tmp(size + 1);
		for (int i = 0;i <= size;i++) {
			sa[i] = i;
			rank[i] = i < size ? s[i] : 0;
		}

		auto compare = [&](int i, int j) {
			if (rank[i] != rank[j]) return rank[i] < rank[j];
			int rank_i = i + k <= size ? rank[i + k] : -1;
			int rank_j = j + k <= size ? rank[j + k] : -1;
			return rank_i < rank_j;
		};

		for (k = 1;k <= size;k *= 2) {
			// ::std::sort(sa.begin(), sa.end(), compare);
			LSD_RadixSort<200000, 1>(sa.begin(), sa.end(),
				[&](int x, int d) {return x + k < rank.size() ? rank[x + k] : 0;});
			LSD_RadixSort<200000, 1>(sa.begin(), sa.end(),
				[&](int x, int d) {return rank[x];});

			tmp[sa[0]] = 0;
			for (int i = 1;i <= size;i++) {
				tmp[sa[i]] = tmp[sa[i - 1]] + (compare(sa[i - 1], sa[i]) ? 1 : 0);
			}
			::std::swap(rank, tmp);
		}
		return sa;
	}

	::std::vector<int> build_lcp() {
		int h = 0;

		for (int i = 0;i < size + 1;i++) {
			if (rank[i] == size) {
				h = 0;
				continue;
			}
			for (int j = sa[rank[i] + 1]; ::std::max(i, j) + h <= size && s[i + h] == s[j + h]; h++);
			_lcp[rank[i]] = h;
			if (h > 0) h--;
		}

		table = ::std::vector<::std::vector<int>>(20, ::std::vector<int>(size + 1));
		for (int i = 0;i <= size;i++) {
			table[0][i] = _lcp[i];
		}

		for (int k = 1;(1 << k) <= size;k++) {
			for (int i = 0;i + (1 << k) <= size;i++) {
				table[k][i] = ::std::min(table[k - 1][i], table[k - 1][i + (1 << (k - 1))]);
			}
		}

		return _lcp;
	}

	int lcp(int i, int j) { // Longest Common Prefix of s[i..] and s[j..]
		i = rank[i];
		j = rank[j];
		if (i > j) ::std::swap(i, j);

		int k = log2[j - i];
		return ::std::min(table[k][i], table[k][j - (1 << k)]);
	}

	int operator[](int k) const {
		return sa[k];
	}

	bool is_upper(T& t, int si) { // True if t > sa[si]
		int ti = 0; si = sa[si];
		while (si < s.size() && ti < t.size()) {
			if (t[ti] > s[si]) return true;
			if (t[ti] < s[si]) return false;
			ti++; si++;
		}
		assert(ti >= t.size() || si >= s.size());
		return (ti < t.size() && si >= s.size());
	}

	int lower_bound(T& t) {
		int l = -1, r = size + 1, m;
		while (r - l > 1) {
			m = (l + r) >> 1;
			if (is_upper(t, m))
				l = m;
			else
				r = m;
		}
		return r;
	}

	int upper_bound(T& t) {
		int l = -1, r = size + 1, m;
		t.back()++;
		while (r - l > 1) {
			m = (l + r) >> 1;
			if (is_upper(t, m))
				l = m;
			else
				r = m;
		}
		t.back()--;
		return r;
	}

	::std::pair<int, int> bounds(T& t) {
		return ::std::pair<int, int>(lower_bound(t), upper_bound(t));
	}
};

template<typename T, typename E>
class SegTree {
private:
	using F = std::function<T(T, T)>;
	using G = std::function<T(T, E)>;
	int n;
	F f;
	G g;
	T ti; // e0:F
	std::vector<T> node;
public:
	SegTree() {}
	SegTree(int _n, F f, G g, T ti) :f(f), g(g), ti(ti) {
		init(_n);
	}
	SegTree(std::vector<T> v, F f, G g, T ti) :f(f), g(g), ti(ti) {
		init(v.size());
		for (int i = 0;i < v.size();i++) node[i + n - 1] = v[i];
		for (int i = n - 2;i >= 0;i--) node[i] = merge(node[i * 2 + 1], node[i * 2 + 2]);
	}

	inline void init(int _n) {
		n = 1;
		while (n < _n) n *= 2;
		node.resize(2 * n - 1, ti);
	}

	inline T merge(T lhs, T rhs) {
		if (lhs == ti) return rhs;
		else if (rhs == ti) return lhs;
		return f(lhs, rhs);
	}

	void update(int k, E x) {
		k += n - 1;
		node[k] = g(node[k], x);
		while (k) {
			k = (k - 1) / 2;
			node[k] = merge(node[k * 2 + 1], node[k * 2 + 2]);
		}
	}

	T query(int a, int b, int k = 0, int l = 0, int r = -1) {
		if (r < 0) r = n;
		if (b <= l || r <= a) return ti;
		if (a <= l && r <= b) return node[k];
		return merge(query(a, b, k * 2 + 1, l, (l + r) / 2), query(a, b, k * 2 + 2, (l + r) / 2, r));
	}
};

int main(void) {
	using namespace std;
	string s[2];
	cin >> s[0];
	s[1] = s[0];
	reverse(s[1].begin(), s[1].end());

	SuffixArray<> SA[2];
	vector<int> sa[2];
	vector<int> rank[2];
	SegTree<int, int> sg[2];

	auto F = [](int a, int b) {return min(a, b);};
	auto G = [](int a, int b) {return b;};

	for (int i = 0;i < 2;i++) {
		SA[i] = SuffixArray<>(s[i]);
		sa[i] = SA[i].build_sa(); SA[i].build_lcp();
		rank[i].resize(sa[i].size());

		for (int j = 0;j < sa[i].size();j++) {
			rank[i][sa[i][j]] = j;
		}
		sg[i] = SegTree<int, int>(sa[i], F, G, numeric_limits<int>::max());
	}

	int m;
	cin >> m;
	for (int i = 0;i < m;i++) {
		string a, b;
		cin >> a >> b;
		reverse(b.begin(), b.end());

		pair<int, int> x = SA[0].bounds(a), y = SA[1].bounds(b);
		int l = sg[0].query(x.first, x.second);
		int r = s[0].size() - sg[1].query(y.first, y.second) - 1;
		if (x.first < x.second && y.first < y.second && l + a.size() <= r + b.size())
			cout << r - l + 1 << endl;
		else
			cout << 0 << endl;
	}
}