#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod1=998244353,mod2=1000000009,MAX=500005,INF=1<<30;

//https://judge.yosupo.jp/submission/41769

#pragma once
#include <algorithm>
#include <cassert>
#include <numeric>
#include <string>
#include <vector>

// CUT begin
// Suffix array algorithms from AtCoder Library
// Document: <https://atcoder.github.io/ac-library/master/document_ja/string.html>
namespace internal {

std::vector<int> sa_naive(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n);
    std::iota(sa.begin(), sa.end(), 0);
    std::sort(sa.begin(), sa.end(), [&](int l, int r) {
        if (l == r) return false;
        while (l < n && r < n) {
            if (s[l] != s[r]) return s[l] < s[r];
            l++, r++;
        }
        return l == n;
    });
    return sa;
}

std::vector<int> sa_doubling(const std::vector<int>& s) {
    int n = int(s.size());
    std::vector<int> sa(n), rnk = s, tmp(n);
    std::iota(sa.begin(), sa.end(), 0);
    for (int k = 1; k < n; k *= 2) {
        auto cmp = [&](int x, int y) {
            if (rnk[x] != rnk[y]) return rnk[x] < rnk[y];
            int rx = x + k < n ? rnk[x + k] : -1;
            int ry = y + k < n ? rnk[y + k] : -1;
            return rx < ry;
        };
        std::sort(sa.begin(), sa.end(), cmp);
        tmp[sa[0]] = 0;
        for (int i = 1; i < n; i++) { tmp[sa[i]] = tmp[sa[i - 1]] + (cmp(sa[i - 1], sa[i]) ? 1 : 0); }
        std::swap(tmp, rnk);
    }
    return sa;
}

// SA-IS, linear-time suffix array construction
// Reference:
// G. Nong, S. Zhang, and W. H. Chan,
// Two Efficient Algorithms for Linear Time Suffix Array Construction
template <int THRESHOLD_NAIVE = 10, int THRESHOLD_DOUBLING = 40> std::vector<int> sa_is(const std::vector<int>& s, int upper) {
    int n = int(s.size());
    if (n == 0) return {};
    if (n == 1) return {0};
    if (n == 2) {
        if (s[0] < s[1]) {
            return {0, 1};
        } else {
            return {1, 0};
        }
    }
    if (n < THRESHOLD_NAIVE) { return sa_naive(s); }
    if (n < THRESHOLD_DOUBLING) { return sa_doubling(s); }

    std::vector<int> sa(n);
    std::vector<bool> ls(n);
    for (int i = n - 2; i >= 0; i--) { ls[i] = (s[i] == s[i + 1]) ? ls[i + 1] : (s[i] < s[i + 1]); }
    std::vector<int> sum_l(upper + 1), sum_s(upper + 1);
    for (int i = 0; i < n; i++) {
        if (!ls[i]) {
            sum_s[s[i]]++;
        } else {
            sum_l[s[i] + 1]++;
        }
    }
    for (int i = 0; i <= upper; i++) {
        sum_s[i] += sum_l[i];
        if (i < upper) sum_l[i + 1] += sum_s[i];
    }

    auto induce = [&](const std::vector<int>& lms) {
        std::fill(sa.begin(), sa.end(), -1);
        std::vector<int> buf(upper + 1);
        std::copy(sum_s.begin(), sum_s.end(), buf.begin());
        for (auto d : lms) {
            if (d == n) continue;
            sa[buf[s[d]]++] = d;
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        sa[buf[s[n - 1]]++] = n - 1;
        for (int i = 0; i < n; i++) {
            int v = sa[i];
            if (v >= 1 && !ls[v - 1]) { sa[buf[s[v - 1]]++] = v - 1; }
        }
        std::copy(sum_l.begin(), sum_l.end(), buf.begin());
        for (int i = n - 1; i >= 0; i--) {
            int v = sa[i];
            if (v >= 1 && ls[v - 1]) { sa[--buf[s[v - 1] + 1]] = v - 1; }
        }
    };

    std::vector<int> lms_map(n + 1, -1);
    int m = 0;
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) { lms_map[i] = m++; }
    }
    std::vector<int> lms;
    lms.reserve(m);
    for (int i = 1; i < n; i++) {
        if (!ls[i - 1] && ls[i]) { lms.push_back(i); }
    }

    induce(lms);

    if (m) {
        std::vector<int> sorted_lms;
        sorted_lms.reserve(m);
        for (int v : sa) {
            if (lms_map[v] != -1) sorted_lms.push_back(v);
        }
        std::vector<int> rec_s(m);
        int rec_upper = 0;
        rec_s[lms_map[sorted_lms[0]]] = 0;
        for (int i = 1; i < m; i++) {
            int l = sorted_lms[i - 1], r = sorted_lms[i];
            int end_l = (lms_map[l] + 1 < m) ? lms[lms_map[l] + 1] : n;
            int end_r = (lms_map[r] + 1 < m) ? lms[lms_map[r] + 1] : n;
            bool same = true;
            if (end_l - l != end_r - r) {
                same = false;
            } else {
                while (l < end_l) {
                    if (s[l] != s[r]) { break; }
                    l++;
                    r++;
                }
                if (l == n || s[l] != s[r]) same = false;
            }
            if (!same) rec_upper++;
            rec_s[lms_map[sorted_lms[i]]] = rec_upper;
        }

        auto rec_sa = sa_is<THRESHOLD_NAIVE, THRESHOLD_DOUBLING>(rec_s, rec_upper);

        for (int i = 0; i < m; i++) { sorted_lms[i] = lms[rec_sa[i]]; }
        induce(sorted_lms);
    }
    return sa;
}

} // namespace internal

std::vector<int> suffix_array(const std::vector<int>& s, int upper) {
    assert(0 <= upper);
    for (int d : s) { assert(0 <= d && d <= upper); }
    auto sa = internal::sa_is(s, upper);
    return sa;
}

template <class T> std::vector<int> suffix_array(const std::vector<T>& s) {
    int n = int(s.size());
    std::vector<int> idx(n);
    iota(idx.begin(), idx.end(), 0);
    sort(idx.begin(), idx.end(), [&](int l, int r) { return s[l] < s[r]; });
    std::vector<int> s2(n);
    int now = 0;
    for (int i = 0; i < n; i++) {
        if (i && s[idx[i - 1]] != s[idx[i]]) now++;
        s2[idx[i]] = now;
    }
    return internal::sa_is(s2, now);
}

std::vector<int> suffix_array(const std::string& s) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) { s2[i] = s[i]; }
    return internal::sa_is(s2, 255);
}

// Reference:
// T. Kasai, G. Lee, H. Arimura, S. Arikawa, and K. Park,
// Linear-Time Longest-Common-Prefix Computation in Suffix Arrays and Its
// Applications
template <class T> std::vector<int> lcp_array(const std::vector<T>& s, const std::vector<int>& sa) {
    int n = int(s.size());
    assert(n >= 1);
    std::vector<int> rnk(n);
    for (int i = 0; i < n; i++) { rnk[sa[i]] = i; }
    std::vector<int> lcp(n - 1);
    int h = 0;
    for (int i = 0; i < n; i++) {
        if (h > 0) h--;
        if (rnk[i] == 0) continue;
        int j = sa[rnk[i] - 1];
        for (; j + h < n && i + h < n; h++) {
            if (s[j + h] != s[i + h]) break;
        }
        lcp[rnk[i] - 1] = h;
    }
    return lcp;
}

std::vector<int> lcp_array(const std::string& s, const std::vector<int>& sa) {
    int n = int(s.size());
    std::vector<int> s2(n);
    for (int i = 0; i < n; i++) { s2[i] = s[i]; }
    return lcp_array(s2, sa);
}

// Count keyword occurence in str
// Complexity: O(min(|str|, |keyword|) * lg |str|)
int count_keyword_occurence(const std::string& str, const std::vector<int>& suffarr, const std::string& keyword) {
    const int n = str.size(), m = keyword.size();
    assert(n == suffarr.size());
    if (n < m) return 0;
    auto f1 = [&](int h) {
        for (int j = 0; h + j < n and j < m; j++) {
            if (str[h + j] < keyword[j]) return true;
            if (str[h + j] > keyword[j]) return false;
        }
        return n - h < m;
    };
    auto f2 = [&](int h) {
        for (int j = 0; h + j < n and j < m; j++) {
            // if (str[h + j] < keyword[j]) return true;
            if (str[h + j] > keyword[j]) return false;
        }
        return true;
    };
    const auto L = std::partition_point(suffarr.begin(), suffarr.end(), f1);
    const auto R = std::partition_point(L, suffarr.end(), f2);
    return std::distance(L, R);
    // return std::vector<int>(L, R); // if you need occurence positions
}
#pragma once
#include <algorithm>
#include <cassert>
#include <vector>

// CUT begin
// Range Minimum Query for static sequence by sparse table
// Complexity: O(NlogN) for precalculation, O(1) per query
template <typename T> struct StaticRMQ {
    inline T func(const T &l, const T &r) const noexcept { return std::min<T>(l, r); }
    int N, lgN;
    T defaultT;
    std::vector<std::vector<T>> data;
    std::vector<int> lgx_table;
    StaticRMQ() = default;
    StaticRMQ(const std::vector<T> &sequence, T defaultT) : N(sequence.size()), defaultT(defaultT) {
        lgx_table.resize(N + 1);
        for (int i = 2; i < N + 1; i++) lgx_table[i] = lgx_table[i >> 1] + 1;
        lgN = lgx_table[N] + 1;
        data.assign(lgN, std::vector<T>(N, defaultT));
        data[0] = sequence;
        for (int d = 1; d < lgN; d++) {
            for (int i = 0; i + (1 << d) <= N; i++) {
                data[d][i] = func(data[d - 1][i], data[d - 1][i + (1 << (d - 1))]);
            }
        }
    }
    T get(int l, int r) const { // [l, r), 0-indexed
        assert(l >= 0 and r <= N);
        if (l >= r) return defaultT;
        int d = lgx_table[r - l];
        return func(data[d][l], data[d][r - (1 << d)]);
    }
};
#include <algorithm>
#include <utility>
#include <vector>
#include <string>

struct LongestCommonPrefix {
    const int N;
    std::vector<int> sainv; // len = N
    StaticRMQ<int> rmq;
    LongestCommonPrefix(const std::string s) : N(s.size()) {
        auto sa = suffix_array(s);
        auto lcp = lcp_array(s, sa);
        sainv.resize(N);
        for (int i = 0; i < N; i++) sainv[sa[i]] = i;
        rmq = {lcp, N};
    }
    int lcplen(int l1, int l2) const {
        if (l1 == l2) return N - l1;
        if (l1 == N or l2 == N) return 0;
        l1 = sainv[l1], l2 = sainv[l2];
        if (l1 > l2) std::swap(l1, l2);
        return rmq.get(l1, l2);
    }
};
#include <algorithm>
#include <string>
#include <tuple>
#include <utility>
#include <vector>

// CUT begin
// Lyndon factorization based on Duval's algorithm
// **NOT VERIFIED YET**
// Reference:
// [1] K. T. Chen, R. H. Fox, R. C. Lyndon,
//     "Free Differential Calculus, IV. The Quotient Groups of the Lower Central Series,"
//     Annals of Mathematics, 81-95, 1958.
// [2] J. P. Duval, "Factorizing words over an ordered alphabet,"
//     Journal of Algorithms, 4(4), 363-381, 1983.
// - https://cp-algorithms.com/string/lyndon_factorization.html
// - https://qiita.com/nakashi18/items/66882bd6e0127174267a
template <typename T> std::vector<std::pair<int, int>> lyndon_factorization(const std::vector<T> &S) {
    const int N = S.size();
    std::vector<std::pair<int, int>> ret;
    for (int l = 0; l < N;) {
        int i = l, j = i + 1;
        while (j < N and S[i] <= S[j]) i = (S[i] == S[j] ? i + 1 : l), j++;
        ret.emplace_back(l, j - i), l += j - i;
    }
    return ret;
}

std::vector<std::pair<int, int>> lyndon_factorization(const std::string &s) {
    const int N = int(s.size());
    std::vector<int> v(N);
    for (int i = 0; i < N; i++) v[i] = s[i];
    return lyndon_factorization<int>(v);
}

// Compute the longest Lyndon prefix for each suffix s[i:N]
// (Our implementation is $O(N \log N)$)
// Example:
// - `teletelepathy` -> [1,4,1,2,1,4,1,2,1,4,1,2,1]
// Reference:
// [1] H. Bannai et al., "The "Runs" Theorem,"
// SIAM Journal on Computing, 46.5, 1501-1514, 2017.
template <typename String>
std::vector<int> longest_lyndon_prefixes(const String &s, const LongestCommonPrefix &rh) {
    const int N = s.size();
    std::vector<std::pair<int, int>> st{{N, N}};
    std::vector<int> ret(N);
    for (int i = N - 1, j = i; i >= 0; i--, j = i) {
        while (st.size() > 1) {
            int iv = st.back().first, jv = st.back().second;
            int l = rh.lcplen(i, iv);
            if (!(iv + l < N and s[i + l] < s[iv + l])) break;
            j = jv;
            st.pop_back();
        }
        st.emplace_back(i, j);
        ret[i] = j - i + 1;
    }
    return ret;
}

// Compute all runs in given string
// Complexity: $O(N \log N)$ in this implementation (Theoretically $O(N)$ achievable)
// N = 2e5 -> ~800 ms
// Reference:
// [1] H. Bannai et al., "The "Runs" Theorem,"
// SIAM Journal on Computing, 46.5, 1501-1514, 2017.
std::vector<std::tuple<int, int, int>> run_enumerate(std::string s) {
    if (s.empty()) return {};
    LongestCommonPrefix rh(s);
    std::reverse(s.begin(), s.end());
    LongestCommonPrefix rrev(s);
    std::reverse(s.begin(), s.end());
    auto t = s;
    auto lo = *std::min_element(s.begin(), s.end()), hi = *std::max_element(s.begin(), s.end());
    for (auto &c : t) c = hi - (c - lo);
    auto l1 = longest_lyndon_prefixes(s, rh), l2 = longest_lyndon_prefixes(t, rh);
    int N = s.size();
    std::vector<std::tuple<int, int, int>> ret;
    for (int i = 0; i < N; i++) {
        int j = i + l1[i], L = i - rrev.lcplen(N - i, N - j), R = j + rh.lcplen(i, j);
        if (R - L >= (j - i) * 2) ret.emplace_back(j - i, L, R);

        if (l1[i] != l2[i]) {
            j = i + l2[i], L = i - rrev.lcplen(N - i, N - j), R = j + rh.lcplen(i, j);
            if (R - L >= (j  - i) * 2) ret.emplace_back(j - i, L, R);
        }
    }
    std::sort(ret.begin(), ret.end());
    ret.erase(std::unique(ret.begin(), ret.end()), ret.end());
    return ret;
}
#include <iostream>
#include <string>
#define PROBLEM "https://judge.yosupo.jp/problem/runenumerate"
using namespace std;

// https://snuke.hatenablog.com/entry/2014/12/02/235837

vector<int> mana(string S){
    vector<int> R(si(S));
    int c = 0;
    for (int i = 0; i < S.size(); ++i) {
        int l = c - (i-c);
        if (i+R[l] < c+R[c]) {
            R[i] = R[l];
        } else {
            int j = c+R[c] - i;
            while (i-j >= 0 && i+j < S.size() && S[i-j] == S[i+j]) ++j;
            R[i] = j;
            c = i;
        }
    }
    return R;
}

struct Rollinghash{
    string S;
    int n;
    int base1;
    int base2;
    vector<ll> h1,h2,ru1,ru2;
    
    void make(string &T,int ba1,int ba2){
        S=T;
        n=S.size();
        h1.assign(n+1,0);
        h2.assign(n+1,0);
        ru1.assign(n+1,0);
        ru2.assign(n+1,0);
        base1=ba1;
        base2=ba2;
        
        ru1[0]=1;
        ru2[0]=1;
        
        for(int i=1;i<=n;i++){
            h1[i]=h1[i-1]*base1+ll(S[i-1]-'a'+1);
            h1[i]%=mod1;
            
            h2[i]=h2[i-1]*base2+ll(S[i-1]-'a'+1);
            h2[i]%=mod2;
            
            ru1[i]=ru1[i-1]*base1%mod1;
            ru2[i]=ru2[i-1]*base2%mod2;
        }
    }
    
    pair<ll,ll> ha(int l,int r){
        pair<ll,ll> res;
        res.fi=(h1[r]-h1[l]*ru1[r-l]%mod1+mod1)%mod1;
        res.se=(h2[r]-h2[l]*ru2[r-l]%mod2+mod2)%mod2;
        
        return res;
    }//開区間
};

// BIT セグ木 遅延セグ木 のみ

// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)

#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
    namespace internal {
        int ceil_pow2(int n) {
            int x = 0;
            while ((1U << x) < (unsigned int)(n)) x++;
            return x;
        }
        int bsf(unsigned int n) {
#ifdef _MSC_VER
            unsigned long index;
            _BitScanForward(&index, n);
            return index;
#else
            return __builtin_ctz(n);
#endif
        }
    }  // namespace internal
    
}  // namespace atcoder

#include <cassert>
#include <numeric>
#include <type_traits>

namespace atcoder {
    
    namespace internal {
        
#ifndef _MSC_VER
        template <class T>
        using is_signed_int128 =
        typename std::conditional<std::is_same<T, __int128_t>::value ||
        std::is_same<T, __int128>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using is_unsigned_int128 =
        typename std::conditional<std::is_same<T, __uint128_t>::value ||
        std::is_same<T, unsigned __int128>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using make_unsigned_int128 =
        typename std::conditional<std::is_same<T, __int128_t>::value,
        __uint128_t,
        unsigned __int128>;
        
        template <class T>
        using is_integral = typename std::conditional<std::is_integral<T>::value ||
        is_signed_int128<T>::value ||
        is_unsigned_int128<T>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                         std::is_signed<T>::value) ||
        is_signed_int128<T>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using is_unsigned_int =
        typename std::conditional<(is_integral<T>::value &&
                                   std::is_unsigned<T>::value) ||
        is_unsigned_int128<T>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using to_unsigned = typename std::conditional<
        is_signed_int128<T>::value,
        make_unsigned_int128<T>,
        typename std::conditional<std::is_signed<T>::value,
        std::make_unsigned<T>,
        std::common_type<T>>::type>::type;
        
#else
        
        template <class T> using is_integral = typename std::is_integral<T>;
        
        template <class T>
        using is_signed_int =
        typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using is_unsigned_int =
        typename std::conditional<is_integral<T>::value &&
        std::is_unsigned<T>::value,
        std::true_type,
        std::false_type>::type;
        
        template <class T>
        using to_unsigned = typename std::conditional<is_signed_int<T>::value,
        std::make_unsigned<T>,
        std::common_type<T>>::type;
        
#endif
        
        template <class T>
        using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
        
        template <class T>
        using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
        
        template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
        
    }  // namespace internal
    
}  // namespace atcoder

#include <cassert>
#include <vector>

namespace atcoder {
    
    template <class T> struct fenwick_tree {
        using U = internal::to_unsigned_t<T>;
        
    public:
        fenwick_tree() : _n(0) {}
        fenwick_tree(int n) : _n(n), data(n) {}
        
        void add(int p, T x) {
            assert(0 <= p && p < _n);
            p++;
            while (p <= _n) {
                data[p - 1] += U(x);
                p += p & -p;
            }
        }
        
        T sum(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            return sum(r) - sum(l);
        }
        
    private:
        int _n;
        std::vector<U> data;
        
        U sum(int r) {
            U s = 0;
            while (r > 0) {
                s += data[r - 1];
                r -= r & -r;
            }
            return s;
        }
    };
    
}  // namespace atcoder


#include <algorithm>
#include <cassert>
#include <iostream>
#include <vector>
namespace atcoder {
    
    template <class S,
    S (*op)(S, S),
    S (*e)(),
    class F,
    S (*mapping)(F, S),
    F (*composition)(F, F),
    F (*id)()>
    struct lazy_segtree {
    public:
        lazy_segtree() : lazy_segtree(0) {}
        lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}
        lazy_segtree(const std::vector<S>& v) : _n(int(v.size())) {
            log = internal::ceil_pow2(_n);
            size = 1 << log;
            d = std::vector<S>(2 * size, e());
            lz = std::vector<F>(size, id());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update(i);
            }
        }
        
        void set(int p, S x) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = x;
            for (int i = 1; i <= log; i++) update(p >> i);
        }
        
        S get(int p) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            return d[p];
        }
        
        S prod(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return e();
            
            l += size;
            r += size;
            
            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push(r >> i);
            }
            
            S sml = e(), smr = e();
            while (l < r) {
                if (l & 1) sml = op(sml, d[l++]);
                if (r & 1) smr = op(d[--r], smr);
                l >>= 1;
                r >>= 1;
            }
            
            return op(sml, smr);
        }
        
        S all_prod() { return d[1]; }
        
        void apply(int p, F f) {
            assert(0 <= p && p < _n);
            p += size;
            for (int i = log; i >= 1; i--) push(p >> i);
            d[p] = mapping(f, d[p]);
            for (int i = 1; i <= log; i++) update(p >> i);
        }
        void apply(int l, int r, F f) {
            assert(0 <= l && l <= r && r <= _n);
            if (l == r) return;
            
            l += size;
            r += size;
            
            for (int i = log; i >= 1; i--) {
                if (((l >> i) << i) != l) push(l >> i);
                if (((r >> i) << i) != r) push((r - 1) >> i);
            }
            
            {
                int l2 = l, r2 = r;
                while (l < r) {
                    if (l & 1) all_apply(l++, f);
                    if (r & 1) all_apply(--r, f);
                    l >>= 1;
                    r >>= 1;
                }
                l = l2;
                r = r2;
            }
            
            for (int i = 1; i <= log; i++) {
                if (((l >> i) << i) != l) update(l >> i);
                if (((r >> i) << i) != r) update((r - 1) >> i);
            }
        }
        
        template <bool (*g)(S)> int max_right(int l) {
            return max_right(l, [](S x) { return g(x); });
        }
        template <class G> int max_right(int l, G g) {
            assert(0 <= l && l <= _n);
            assert(g(e()));
            if (l == _n) return _n;
            l += size;
            for (int i = log; i >= 1; i--) push(l >> i);
            S sm = e();
            do {
                while (l % 2 == 0) l >>= 1;
                if (!g(op(sm, d[l]))) {
                    while (l < size) {
                        push(l);
                        l = (2 * l);
                        if (g(op(sm, d[l]))) {
                            sm = op(sm, d[l]);
                            l++;
                        }
                    }
                    return l - size;
                }
                sm = op(sm, d[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }
        
        template <bool (*g)(S)> int min_left(int r) {
            return min_left(r, [](S x) { return g(x); });
        }
        template <class G> int min_left(int r, G g) {
            assert(0 <= r && r <= _n);
            assert(g(e()));
            if (r == 0) return 0;
            r += size;
            for (int i = log; i >= 1; i--) push((r - 1) >> i);
            S sm = e();
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (!g(op(d[r], sm))) {
                    while (r < size) {
                        push(r);
                        r = (2 * r + 1);
                        if (g(op(d[r], sm))) {
                            sm = op(d[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - size;
                }
                sm = op(d[r], sm);
            } while ((r & -r) != r);
            return 0;
        }
        
    private:
        int _n, size, log;
        std::vector<S> d;
        std::vector<F> lz;
        
        void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
        void all_apply(int k, F f) {
            d[k] = mapping(f, d[k]);
            if (k < size) lz[k] = composition(f, lz[k]);
        }
        void push(int k) {
            all_apply(2 * k, lz[k]);
            all_apply(2 * k + 1, lz[k]);
            lz[k] = id();
        }
    };
    
}  // namespace atcoder

#include <algorithm>
#include <cassert>
#include <vector>

namespace atcoder {
    
    template <class S, S (*op)(S, S), S (*e)()> struct segtree {
    public:
        segtree() : segtree(0) {}
        segtree(int n) : segtree(std::vector<S>(n, e())) {}
        segtree(const std::vector<S>& v) : _n(int(v.size())) {
            log = internal::ceil_pow2(_n);
            size = 1 << log;
            d = std::vector<S>(2 * size, e());
            for (int i = 0; i < _n; i++) d[size + i] = v[i];
            for (int i = size - 1; i >= 1; i--) {
                update(i);
            }
        }
        
        void set(int p, S x) {
            assert(0 <= p && p < _n);
            p += size;
            d[p] = x;
            for (int i = 1; i <= log; i++) update(p >> i);
        }
        
        S get(int p) {
            assert(0 <= p && p < _n);
            return d[p + size];
        }
        
        S prod(int l, int r) {
            assert(0 <= l && l <= r && r <= _n);
            S sml = e(), smr = e();
            l += size;
            r += size;
            
            while (l < r) {
                if (l & 1) sml = op(sml, d[l++]);
                if (r & 1) smr = op(d[--r], smr);
                l >>= 1;
                r >>= 1;
            }
            return op(sml, smr);
        }
        
        S all_prod() { return d[1]; }
        
        template <bool (*f)(S)> int max_right(int l) {
            return max_right(l, [](S x) { return f(x); });
        }
        template <class F> int max_right(int l, F f) {
            assert(0 <= l && l <= _n);
            assert(f(e()));
            if (l == _n) return _n;
            l += size;
            S sm = e();
            do {
                while (l % 2 == 0) l >>= 1;
                if (!f(op(sm, d[l]))) {
                    while (l < size) {
                        l = (2 * l);
                        if (f(op(sm, d[l]))) {
                            sm = op(sm, d[l]);
                            l++;
                        }
                    }
                    return l - size;
                }
                sm = op(sm, d[l]);
                l++;
            } while ((l & -l) != l);
            return _n;
        }
        
        template <bool (*f)(S)> int min_left(int r) {
            return min_left(r, [](S x) { return f(x); });
        }
        template <class F> int min_left(int r, F f) {
            assert(0 <= r && r <= _n);
            assert(f(e()));
            if (r == 0) return 0;
            r += size;
            S sm = e();
            do {
                r--;
                while (r > 1 && (r % 2)) r >>= 1;
                if (!f(op(d[r], sm))) {
                    while (r < size) {
                        r = (2 * r + 1);
                        if (f(op(d[r], sm))) {
                            sm = op(d[r], sm);
                            r--;
                        }
                    }
                    return r + 1 - size;
                }
                sm = op(d[r], sm);
            } while ((r & -r) != r);
            return 0;
        }
        
    private:
        int _n, size, log;
        std::vector<S> d;
        
        void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
    };
    
}  // namespace atcoder

using T=pair<int,int>;

T f(T a,T b){
    return mp(min(a.fi,b.fi),max(a.se,b.se));
}

T ti(){
    return mp(INF,-INF);
}

vector<pair<int,int>> wh[MAX];

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    int N;string S;
    cin >> N;
    cin >> S;
    int Q;cin>>Q;
    vector<pair<int,int>> que(Q);
    for(int i=0;i<Q;i++){
        int a,b;cin>>a>>b;a--;
        que[i]=mp(a,b);
    }
    vector<pair<int,int>> ans(Q,mp(INF,0));
    
    for(int q=0;q<2;q++){
        for(int i=0;i<MAX;i++) wh[i].clear();
        auto v = LongestCommonPrefix(S);
        auto ret = run_enumerate(S);
        for(auto p:ret){
            auto [t,l,r]=p;
            wh[t].push_back(mp(l,r));
            //cout<<t<<" "<<l<<" "<<r<<endl;
        }
        
        for(int i=1;i<MAX;i++) sort(all(wh[i]));
        
        ll ha1=37,ha2=43;
        Rollinghash ro1,ro2;
        ro1.make(S,ha1,ha2);
        reverse(all(S));
        ro2.make(S,ha1,ha2);
        reverse(all(S));
        
        vector<int> maki=mana(S);
        string SSS;
        for(int i=0;i<N;i++){
            if(i) SSS+='$';
            SSS+=S[i];
        }
        vector<int> magu=mana(SSS);
        
        vector<pair<int,int>> defki,defgu;
        for(int i=0;i<N;i++){
            defki.push_back(mp(i-(maki[i]-1),i+(maki[i]-1)));
        }
        for(int i=1;i<si(magu);i+=2){
            if(magu[i]<=1) defgu.push_back(mp(INF-1,-INF+1));
            else defgu.push_back(mp(i/2-(magu[i]/2-1),i/2+1+(magu[i]/2-1)));
        }
        
        //for(auto [a,b]:defki) cout<<a<<" "<<b<<endl;
        
        //for(auto [a,b]:defgu) cout<<a<<" "<<b<<endl;
        
        atcoder::segtree<T,f,ti> segki(defki),seggu(defgu);
        
        for(int qq=0;qq<Q;qq++){
            auto [l,r]=que[qq];
            int L=0,R=r-l+1;
            while(R-L>1){
                int M=(L+R)/2;
                auto a=ro1.ha(l,l+M),b=ro2.ha(N-r,N-r+M);
                if(a==b) L=M;
                else R=M;
            }
            if(L==r-l) ans[qq].fi=0;
            else{
                int x=l+L,y=r-L;
                int len=y-x;
                {
                    int lenki=(len+1)/2;
                    int left=y-lenki-1,right=y-1;
                    while(right-left>1){
                        int mid=(left+right)/2;
                        auto re=segki.prod(y-lenki,mid+1);
                        if(re.se>=y-1) right=mid;
                        else left=mid;
                    }
                    int sakuL=x,sakuR=y-((y-right)*2-1); //[)
                    
                    if(chmin(ans[qq].fi,sakuR-sakuL)) ans[qq].se=0;
                    
                    if(ans[qq].fi==sakuR-sakuL){
                        int misyu=INF;
                        for(int a=1;a*a<=sakuR-sakuL;a++){
                            if((sakuR-sakuL)%a) continue;
                            {
                                auto it=lower_bound(all(wh[a]),mp(sakuL,INF));
                                if(it!=wh[a].begin()){
                                    it--;
                                    if((*it).fi<=sakuL&&(*it).se>=sakuR) chmin(misyu,a);
                                }
                            }
                            {
                                auto it=lower_bound(all(wh[(sakuR-sakuL)/a]),mp(sakuL,INF));
                                if(it!=wh[(sakuR-sakuL)/a].begin()){
                                    it--;
                                    if((*it).fi<=sakuL&&(*it).se>=sakuR) chmin(misyu,(sakuR-sakuL)/a);
                                }
                            }
                        }
                        
                        if(misyu<=sakuR-sakuL){
                            int a=misyu;
                            auto it=lower_bound(all(wh[a]),mp(sakuL,INF));
                            if(it!=wh[a].begin()){
                                it--;
                                int cn=(sakuL-max(l,(*it).fi)+a-1)/a+1;
                                if(cn>2){
                                    int lele=sakuL-max(l,(*it).fi);
                                    if(1){
                                        ans[qq].se+=lele+1;
                                    }else{
                                        ans[qq].se+=cn;
                                    }
                                }
                                else{
                                    ans[qq].se++;
                                    int le=l-1,ri=sakuL;
                                    while(ri-le>1){
                                        int mi=(le+ri)/2;
                                        if(sakuR-sakuL<sakuL-mi) le=mi;
                                        else{
                                            auto a=ro1.ha(mi,sakuL);
                                            auto b=ro1.ha(sakuR-(sakuL-mi),sakuR);
                                            if(a==b) ri=mi;
                                            else le=mi;
                                        }
                                    }
                                    ans[qq].se+=sakuL-ri;
                                }
                            }
                        }else{
                            ans[qq].se++;
                            int le=l-1,ri=sakuL;
                            while(ri-le>1){
                                int mi=(le+ri)/2;
                                if(sakuR-sakuL<sakuL-mi) le=mi;
                                else{
                                    auto a=ro1.ha(mi,sakuL);
                                    auto b=ro1.ha(sakuR-(sakuL-mi),sakuR);
                                    if(a==b) ri=mi;
                                    else le=mi;
                                }
                            }
                            ans[qq].se+=sakuL-ri;
                        }
                    }
                }
                if(len>=2){
                    int lengu=(len)/2;
                    int left=y-lengu-2,right=y-1;
                    while(right-left>1){
                        int mid=(left+right)/2;
                        auto re=seggu.prod(y-lengu-1,mid+1);
                        if(re.se>=y-1) right=mid;
                        else left=mid;
                    }
                    if(right==y-1) continue;
                    
                    int sakuL=x,sakuR=y-((y-right-1)*2); //[)
                    
                    if(chmin(ans[qq].fi,sakuR-sakuL)) ans[qq].se=0;
                    
                    if(ans[qq].fi==sakuR-sakuL){
                        int misyu=INF;
                        for(int a=1;a*a<=sakuR-sakuL;a++){
                            if((sakuR-sakuL)%a) continue;
                            {
                                auto it=lower_bound(all(wh[a]),mp(sakuL,INF));
                                if(it!=wh[a].begin()){
                                    it--;
                                    if((*it).fi<=sakuL&&(*it).se>=sakuR) chmin(misyu,a);
                                }
                            }
                            {
                                auto it=lower_bound(all(wh[(sakuR-sakuL)/a]),mp(sakuL,INF));
                                if(it!=wh[(sakuR-sakuL)/a].begin()){
                                    it--;
                                    if((*it).fi<=sakuL&&(*it).se>=sakuR) chmin(misyu,(sakuR-sakuL)/a);
                                }
                            }
                        }
                        
                        if(misyu<=sakuR-sakuL){
                            int a=misyu;
                            auto it=lower_bound(all(wh[a]),mp(sakuL,INF));
                            if(it!=wh[a].begin()){
                                it--;
                                int cn=(sakuL-max(l,(*it).fi)+a-1)/a+1;
                                if(cn>2){
                                    int lele=sakuL-max(l,(*it).fi);
                                    if(1){
                                        ans[qq].se+=lele+1;
                                    }else{
                                        ans[qq].se+=cn;
                                    }
                                }
                                else{
                                    ans[qq].se++;
                                    int le=l-1,ri=sakuL;
                                    while(ri-le>1){
                                        int mi=(le+ri)/2;
                                        if(sakuR-sakuL<sakuL-mi) le=mi;
                                        else{
                                            auto a=ro1.ha(mi,sakuL);
                                            auto b=ro1.ha(sakuR-(sakuL-mi),sakuR);
                                            if(a==b) ri=mi;
                                            else le=mi;
                                        }
                                    }
                                    ans[qq].se+=sakuL-ri;
                                }
                            }
                        }else{
                            ans[qq].se++;
                            int le=l-1,ri=sakuL;
                            while(ri-le>1){
                                int mi=(le+ri)/2;
                                if(sakuR-sakuL<sakuL-mi) le=mi;
                                else{
                                    auto a=ro1.ha(mi,sakuL);
                                    auto b=ro1.ha(sakuR-(sakuL-mi),sakuR);
                                    if(a==b) ri=mi;
                                    else le=mi;
                                }
                            }
                            ans[qq].se+=sakuL-ri;
                        }
                    }
                }
            }
        }
        
        reverse(all(S));
        for(int qq=0;qq<Q;qq++){
            swap(que[qq].fi,que[qq].se);
            que[qq].fi=N-que[qq].fi;
            que[qq].se=N-que[qq].se;
        }
    }
    
    for(int q=0;q<Q;q++){
        if(ans[q].fi==0) cout<<0<<" "<<0<<"\n";
        else cout<<ans[q].fi<<" "<<ans[q].se<<"\n";
    }
    
}