Problem:
Score : 400 points

Problem Statement

Joisino is planning to record N TV programs with recorders.

The TV can receive C channels numbered 1 through C.

The i-th program that she wants to record will be broadcast from time s_i to time t_i (including time s_i but not t_i) on Channel c_i.

Here, there will never be more than one program that are broadcast on the same channel at the same time.

When the recorder is recording a channel from time S to time T (including time S but not T), it cannot record other channels from time S-0.5 to time T (including time S-0.5 but not T).

Find the minimum number of recorders required to record the channels so that all the N programs are completely recorded.

Constraints

1≤N≤10^5

1≤C≤30

1≤s_i<t_i≤10^5

1≤c_i≤C

If c_i=c_j and i≠j, either t_i≤s_j or s_i≥t_j.

All input values are integers.

Input

Input is given from Standard Input in the following format:

N C
s_1 t_1 c_1
:
s_N t_N c_N

Output

When the minimum required number of recorders is x, print the value of x.

Sample Input 1

3 2
1 7 2
7 8 1
8 12 1

Sample Output 1

2

Two recorders can record all the programs, for example, as follows:

With the first recorder, record Channel 2 from time 1 to time 7. The first program will be recorded. Note that this recorder will be unable to record other channels from time 0.5 to time 7.

With the second recorder, record Channel 1 from time 7 to time 12. The second and third programs will be recorded. Note that this recorder will be unable to record other channels from time 6.5 to time 12.

Sample Input 2

3 4
1 3 2
3 4 4
1 4 3

Sample Output 2

3

There may be a channel where there is no program to record.

Sample Input 3

9 4
56 60 4
33 37 2
89 90 3
32 43 1
67 68 3
49 51 3
31 32 3
70 71 1
11 12 3

Sample Output 3

2

Solution in C++11 (GCC 4.8.1) (judge verdict: Accepted)

#include<cstdio>
#include<vector>
#include<queue>
#include<map>
#include<set>
#include<unordered_map>
#include<stack>
#include<string>
#include<algorithm>
#include<functional>
#include<cstring>
#include<complex>
using namespace std;

/**** Type Define ****/

typedef long long ll;
typedef pair<ll, ll> P;
typedef pair<ll, P> Q;
typedef complex<double> C;

/**** Macro Define ****/

#define cx real()
#define cy imag()

/**** Const List   ****/

const ll INF = 1LL << 60;
const double DINF = 1e30;
const ll mod = 1000000007;
const ll MAX_FLOW_MAX_V = 10000;
const ll MIN_COST_FLOW_MAX_V = 10000;
const ll BIPARTITE_MATCHING_MAX_V = 10000;
const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, -1, 0, 1};
const C I = C(0, 1);
const double EPS = 1e-10;

/**** General Functions ****/

template <typename T>
T tmin(T a, T b) { return a > b ? b : a; };

template <typename T>
T tmax(T a, T b) { return a > b ? a : b; };

template <typename T>
T tadd(T a, T b) { return a + b; };

template <typename T>
T tmul(T a, T b) { return a * b; };

template <typename T>
T tpow(T a, T b) { return a * b; };

ll gcd(ll a, ll b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}

ll extgcd(ll a, ll b, ll& x, ll& y) {
  if (b == 0) {
    x = 1, y = 0; return a;
  }
  ll q = a/b, g = extgcd(b, a - q*b, x, y);
  ll z = x - q * y;
  x = y;
  y = z;
  return g;
}

ll invmod (ll a, ll m) { // a^-1 mod m
  ll x, y;
  extgcd(a, m, x, y);
  x %= m;
  if (x < 0) x += m;
  return x;
}

ll nCk(ll n, ll k, ll mod) {
  ll ans = 1;
  for (ll i = n, j = 1; j <= k; i--, j++) ans = (((ans * i) % mod) * invmod(j, mod)) % mod;
  return ans;
}

ll lmin(ll a, ll b) { return a > b ? b : a; };

ll lmax(ll a, ll b) { return a > b ? a : b; };

ll lsum(ll a, ll b) { return a + b; };

/**** Matrix ****/

template <typename T>
struct Matrix {
  typedef vector<T> vec;
  typedef vector<vec> mat;
  ll x, y; // x: horizon  y: vertical
  mat d;

  Matrix(ll _y, ll _x = -1) {
    if (_x == -1) _x = _y;
    x = _x, y = _y;
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) d[i][j] = 0;
  }
  void unit() {
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) d[i][j] = i == j ? 1 : 0;
  }
  Matrix copy() {
    Matrix m(y, x);
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) m.d[i][j] = d[i][j];
    return m;
  }
  Matrix<T> operator + (Matrix<T>& t) { // No error check! Don't forget to check Matrix size!!
    Matrix<T> m(y, x);
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) m.d[i][j] = d[i][j] + t.d[i][j];
    return m;
  }
  Matrix<T> operator - (Matrix<T>& t) {
    Matrix<T> m(y, x);
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) m.d[i][j] = d[i][j] - t.d[i][j];
    return m;
  }
  Matrix<T> operator * (T t) {
    Matrix<T> m(y, x);
    for (int i = 0; i < y; i++) for (int j = 0; j < x; j++) m.d[i][j] = d[i][j] * t;
    return m;
  }
  Matrix<T> det(Matrix<T>& t) { // x need to correspond to t.y
    Matrix<T> m(y, x);
    for (int i = 0; i < y; i++)
      for (int j = 0; j < x; j++)
        for (int k = 0; k < t.x; k++) m.d[i][j] += d[i][k] * t.d[k][j]; ////////////// mod???
    return m;
  }
};

/**** Zip ****/

template <typename T>
class Zip {
  vector<T> d;
  bool flag;
public:
  Zip() {
    flag = false;
  }
  void add(T x) {
    d.push_back(x);
    flag = true;
  }
  ll getNum(T x) { // T need to have operator < !!
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return lower_bound(d.begin(), d.end(), x) - d.begin();
  }
  ll size() {
    if (flag) {
      sort(d.begin(), d.end());
      d.erase(unique(d.begin(), d.end()), d.end());
      flag = false;
    }
    return (ll)d.size();
  }
};

/**** Union Find ****/

class UnionFind {
  vector<ll> par, rank; // par > 0: number, par < 0: -par
public:
  void init(ll n) {
    par.resize(n, 1); rank.resize(n, 0);
  }
  ll getSize(ll x) {
    return par[find(x)];
  }
  ll find(ll x) {
    if (par[x] > 0) return x;
    return -(par[x] = -find(-par[x]));
  }
  void merge(ll x, ll y) {
    x = find(x);
    y = find(y);
    if (x == y) return;
    if (rank[x] < rank[y]) {
      par[y] += par[x];
      par[x] = -y;
    } else {
      par[x] += par[y];
      par[y] = -x;
      if (rank[x] == rank[y]) rank[x]++;
    }
  }
  bool isSame(ll x, ll y) {
    return find(x) == find(y);
  }
};

template <typename T>
struct UnionFindT {
  vector<ll> par;
  vector<ll> rank;
  vector<T> diff_weight;

  UnionFindT(ll n = 1, T SUM_UNITY = 0) {
    init(n, SUM_UNITY);
  }

  void init(ll n = 1, T SUM_UNITY = 0) {
    par.resize(n); rank.resize(n); diff_weight.resize(n);
    for (ll i = 0; i < n; ++i) par[i] = i, rank[i] = 0, diff_weight[i] = SUM_UNITY;
  }

  ll find(ll x) {
    if (par[x] == x) {
      return x;
    }
    else {
      ll r = find(par[x]);
        diff_weight[x] += diff_weight[par[x]];
        return par[x] = r;
    }
  }

  T weight(ll x) {
    find(x);
    return diff_weight[x];
  }

  bool isSame(ll x, ll y) {
    return find(x) == find(y);
  }

  bool merge(ll x, ll y, T w) {
    w += weight(x); w -= weight(y);
    x = find(x); y = find(y);
    if (x == y) return false;
    if (rank[x] < rank[y]) swap(x, y), w = -w;
    if (rank[x] == rank[y]) ++rank[x];
    par[y] = x;
    diff_weight[y] = w;
    return true;
  }

  T diff(ll x, ll y) {
    return weight(y) - weight(x);
  }
};

class PersistentUnionFind {
  vector<ll> rank, fin, par;
  ll index;
public:
  void init(ll n) {
    index = 0;
    par.resize(n); rank.resize(n, 1); fin.resize(n, 0);
    for (ll i = 0; i < n; i++) par[i] = i;
  }
  ll find(ll x, ll t) {
    if (t >= fin[x] && par[x] != x) return find(par[x], t);
    return x;
  }
  void merge(ll x, ll y) {
    x = find(x, index);
    y = find(y, index);
    index++;
    if (x == y) return;
    if (rank[x] < rank[y]) par[x] = y, fin[x] = index;
    else {
      par[y] = x, fin[y] = index;
      if (rank[x] == rank[y]) rank[x]++;
    }
  }
  bool isSame(ll x, ll y, ll t) { return find(x, t) == find(y, t); }
};

/**** Segment Tree ****/

template <typename T>
class SegmentTree {
  ll n;
  vector<T> node;
  function<T(T, T)> fun, fun2;
  bool customChange;
  T outValue, initValue;
public:
  void init(ll num, function<T(T, T)> resultFunction, T init, T out, function<T(T, T)> changeFunction = NULL) {
    // changeFunction: (input, beforevalue) => newvalue
    fun = resultFunction;
    fun2 = changeFunction;
    customChange = changeFunction != NULL;
    n = 1;
    while (n < num) n *= 2;
    node.resize(2 * n - 1, init);
    outValue = out;
    initValue = init;
  }
  void valueChange(ll num, T value) {
    num += n-1;
    if (customChange) node[num] = fun2(value, node[num]);
    else node[num] = value;
    while (num > 0) num = (num - 1) / 2, node[num] = fun(node[num * 2 + 1], node[num * 2 + 2]);
  }
  T rangeQuery(ll a, ll b, ll l = 0, ll r = -1, ll k = 0) { // [a, b)
    if (r == -1) r = n;
    if (a <= l && r <= b) return node[k];
    if (b <= l || r <= a) return outValue;
    ll mid = (l + r) / 2;
    return fun(rangeQuery(a, b, l, mid, 2*k+1), rangeQuery(a, b, mid, r, 2*k+2));
  }
};

template <typename T>
class LazySegmentTree {
  ll n;
  vector<T> node;
  vector<T> lazyNode;
  function<T(T, T)> fun, fun2;
  function<T(T, ll)> fun3;
  T outValue, initValue;
  T substitution(T a, T b) { return a; }
  void eval(ll k, ll l, ll r) {
    if (lazyNode[k] == 0) return;
    node[k] = fun2(fun3(lazyNode[k], r - l), node[k]);
    if (r - l > 1) {
      lazyNode[2 * k + 1] = fun2(lazyNode[k], lazyNode[2 * k + 1]);
      lazyNode[2 * k + 2] = fun2(lazyNode[k], lazyNode[2 * k + 2]);
    }
    lazyNode[k] = initValue;
  }
public:
  void init(ll num, function<T(T, T)> resultFunction, function<T(T, T)> changeFunction, function<T(T, ll)> lazyFunction, T init, T out) {
    // changeFunction: (input, beforevalue) => newvalue
    // lazyFunction: (lazyNode, diff) => newvalue
    fun = resultFunction;
    fun2 = changeFunction;
    fun3 = lazyFunction;
    n = 1;
    while (n < num) n *= 2;
    node.resize(2 * n - 1, init);
    lazyNode.resize(2 * n - 1, init);
    outValue = out;
    initValue = init;
  }
  void rangeChange(ll a, ll b, T value, ll l = 0, ll r = -1, ll k = 0) {
    if (r == -1) r = n;
    eval(k, l, r);
    if (b <= l || r <= a) return;
    if (a <= l && r <= b) {
      lazyNode[k] = fun2(value, lazyNode[k]);
      eval(k, l, r);
    } else {
      ll mid = (l + r) / 2;
      rangeChange(a, b, value, l, mid, 2*k+1);
      rangeChange(a, b, value, mid, r, 2*k+2);
      node[k] = fun(node[2*k+1], node[2*k+2]);
    }
  }
  T rangeQuery(ll a, ll b, ll l = 0, ll r = -1, ll k = 0) { // [a, b)
    if (r == -1) r = n;
    if (b <= l || r <= a) return outValue;
    eval(k, l, r);
    if (a <= l && r <= b) return node[k];
    ll mid = (l + r) / 2;
    return fun(rangeQuery(a, b, l, mid, 2*k+1), rangeQuery(a, b, mid, r, 2*k+2));
  }
};

/**** Network Flow ****/

class MaxFlow {
public:
  struct edge { ll to, cap, rev; };

  vector<edge> G[MAX_FLOW_MAX_V];
  bool used[MAX_FLOW_MAX_V];
  ll level[MAX_FLOW_MAX_V];
  ll iter[MAX_FLOW_MAX_V];
  
  void init() {
    for (ll i = 0; i < MAX_FLOW_MAX_V; i++) {
      G[i].clear();
    }
  }
  void add_edge(ll from, ll to, ll cap) {
    G[from].push_back((edge){to, cap, (ll)G[to].size()});
    G[to].push_back((edge){from, 0, (ll)G[from].size() - 1});
  }
  void add_undirected_edge(ll e1, ll e2, ll cap) {
    G[e1].push_back((edge){e2, cap, (ll)G[e2].size()});
    G[e2].push_back((edge){e1, cap, (ll)G[e1].size() - 1});
  }
  ll dfs(ll v, ll t, ll f) {
    if (v == t) return f;
    used[v] = true;
    for (ll i = 0; i < (ll)G[v].size(); i++) {
      edge &e = G[v][i];
      if (!used[e.to]&& e.cap > 0) {
        ll d = dfs(e.to, t, min(f, e.cap));
        if (d > 0) {
          e.cap -= d;
          G[e.to][e.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }
  ll max_flow(ll s, ll t) {
    ll flow = 0;
    while (1) {
      memset(used, 0, sizeof(used));
      ll f = dfs(s, t, INF);
      if (f == 0) return flow;
      flow += f;
    }
  }
  void bfs(ll s) {
    memset(level, -1, sizeof(level));
    queue<ll> que;
    level[s] = 0;
    que.push(s);
    while (!que.empty()) {
      ll v = que.front(); que.pop();
      for (ll i = 0; i < (ll)G[v].size(); i++) {
        edge &e = G[v][i];
        if (e.cap > 0 && level[e.to] < 0) {
          level[e.to] = level[v] + 1;
          que.push(e.to);
        }
      }
    }
  }
  ll dinic_dfs(ll v, ll t, ll f) {
    if (v == t) return f;
    for (ll &i= iter[v]; i < (ll)G[v].size(); i++) {
      edge &e = G[v][i];
      if (e.cap > 0 && level[v] < level[e.to]) {
        ll d = dinic_dfs(e.to, t, min(f, e.cap));
        if (d > 0) {
          e.cap -= d;
          G[e.to][e.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }
  ll dinic(ll s, ll t) {
    ll flow = 0;
    while (1) {
      bfs(s);
      if (level[t] < 0) return flow;
      memset(iter, 0, sizeof(iter));
      ll f;
      while ((f = dinic_dfs(s, t, INF)) > 0) {
        flow += f;
      }
    }
  }
};

/**** bipartite matching ****/

class BipartiteMatching {
public:
  ll V;
  vector<ll> G[BIPARTITE_MATCHING_MAX_V];
  ll match[BIPARTITE_MATCHING_MAX_V];
  bool used[BIPARTITE_MATCHING_MAX_V];
  
  BipartiteMatching(ll v) {
    V = v;
  }
  void init(ll v) {
    V = v;
    for (ll i = 0; i < BIPARTITE_MATCHING_MAX_V; i++) {
      G[i].clear();
    }
  }
  void add_edge(ll u, ll v) {
    G[u].push_back(v);
    G[v].push_back(u);
  }
  bool dfs(ll v) {
    used[v] = true;
    for (ll i = 0; i < (ll)G[v].size(); i++) {
      ll u = G[v][i], w = match[u];
      if (w < 0 || !used[w] && dfs(w)) {
        match[v] = u;
        match[u] = v;
        return true;
      }
    }
    return false;
  }
  ll max_matching() {
    ll res = 0;
    memset(match, -1, sizeof(match));
    for (ll v = 0; v < V;v++) {
      if (match[v] < 0) {
        memset(used, 0, sizeof(used));
        if (dfs(v)) {
          res++;
        }
      }
    }
    return res;
  }
};

class MinCostFlow {
public:
  struct edge { ll to, cap, cost, rev; };

  ll V;
  vector<edge> G[MIN_COST_FLOW_MAX_V];
  ll dist[MIN_COST_FLOW_MAX_V];
  ll prevv[MIN_COST_FLOW_MAX_V];
  ll preve[MIN_COST_FLOW_MAX_V];
  ll h[MIN_COST_FLOW_MAX_V];

  MinCostFlow(ll v) {
    V = v;
  }
  void init() {
    for (ll i = 0; i < MAX_FLOW_MAX_V; i++) {
      G[i].clear();
    }
  }
  void add_edge(ll from, ll to, ll cap, ll cost) {
    G[from].push_back((edge){to, cap, cost, (ll)G[to].size()});
    G[to].push_back((edge){from, 0, -cost, (ll)G[from].size() - 1});
  }
  void add_undirected_edge(ll e1, ll e2, ll cap, ll cost) {
    add_edge(e1, e2, cap, cost);
    add_edge(e2, e1, cap, cost);
  }
  ll min_cost_flow(ll s, ll t, ll f) { // minas
    ll res = 0;
    while (f > 0) {
      fill(dist, dist + V, INF);
      dist[s] = 0;
      bool update = true;
      while (update) {
        update = false;
        for (ll v = 0; v < V; v++) {
          if (dist[v] == INF) continue;
          for (ll i = 0; i < (ll)G[v].size(); i++) {
            edge &e = G[v][i];
            if (e.cap > 0 && dist[e.to] > dist[v] + e.cost) {
              dist[e.to] = dist[v] + e.cost;
              prevv[e.to] = v;
              preve[e.to] = i;
              update = true;
            }
          }
        }
      }
      if (dist[t] == INF) {
        return -1;
      }
      ll d = f;
      for (ll v = t; v != s; v = prevv[v]) {
        d = min(d, G[prevv[v]][preve[v]].cap);
      }
      f -= d;
      res += d * dist[t];
      for (ll v = t; v != s; v = prevv[v]) {
        edge &e = G[prevv[v]][preve[v]];
        e.cap -= d;
        G[v][e.rev].cap += d;
      }
    }
    return res;
  }
  ll min_cost_flow_dijkstra(ll s, ll t, ll f) {
    ll res = 0;
    fill(h, h + V, 0);
    while (f > 0) {
      priority_queue<P, vector<P>, greater<P> > que;
      fill(dist, dist + V, 0);
      dist[s] = 0;
      que.push(P(0, s));
      while (!que.empty()) {
        P p = que.top(); que.pop();
        int v = p.second;
        if (dist[v] < p.first) continue;
        for (int i = 0; i < G[v].size(); i++) {
          edge &e = G[v][i];
          if (e.cap > 0 && dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
            dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
            prevv[e.to] = v;
            preve[e.to] = i;
            que.push(P(dist[e.to], e.to));
          }
        }
      }
      if (dist[t] == INF) {
        return -1;
      }
      for (int v = 0; v < V; v++) h[v] += dist[v];
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        d = tmin<ll>(d, G[prevv[v]][preve[v]].cap);
      }
      f -= d;
      res += d * h[t];
      for (int v = t; v != s; v = prevv[v]) {
        edge &e = G[prevv[v]][preve[v]];
        e.cap -= d;
        G[v][e.rev].cap += d;
      }
      return res;
    }
    return 0;
  }
};

/**** LIS ****/
ll lis(ll* a, ll n, ll* dp) {
  fill(dp, dp + n, INF);
  for (ll i = 0; i < n; i++) *lower_bound(dp, dp + n, a[i]) = a[i];
  return (ll)(lower_bound(dp, dp + n, INF) - dp);
}

/**** Binary Search ****/

ll binarySearch(function<bool(ll)> check, ll ok, ll ng) {
  while ((ok - ng > 1) || (ng - ok > 1)) {
    ll mid = (ok + ng) / 2;
    if (check(mid)) ok = mid;
    else ng = mid;
  }
  return ok;
}

double binarySearchDouble(function<bool(double)> check, double ok, double ng) {
  while ((ok - ng > EPS) || (ng - ok > EPS)) {
    double mid = (ok + ng) / 2;
    if (check(mid)) ok = mid;
    else ng = mid;
  }
  return ok;
}

/**** Geometry ****/

bool isEqual(double a, double b) { return abs(a - b) < EPS; }
bool isCEqual(C a, C b) { return isEqual(a.cx, a.cy) && isEqual(a.cy, a.cy); }
bool isZero(double a) { return abs(a) < EPS; } // a == 0
bool isUZero(double a) { return a > EPS; } // a > 0
bool isUEZero(double a) { return a > -EPS; } // a >= 0
bool isLZero(double a) { return a < -EPS; } // a < 0
bool isLEZero(double a) { return a < EPS; } // a <= 0
C getUnitVector(C a) { double len = abs(a); return isZero(len) ? C(0.0, 0.0) : a / len; }
double dot(C a, C b) { return a.cx * b.cx + a.cy * b.cy; } // |a||b|cosθ
double det(C a, C b) { return a.cx * b.cy - a.cy * b.cx; } // |a||b|sinθ
bool isLineOrthogonal(C a1, C a2, C b1, C b2) { return isZero(dot(a1 - a2, b1 - b2)); } // a1-a2, b1-b2
bool isLineParallel(C a1, C a2, C b1, C b2) { return isZero(det(a1 - a2, b1 - b2)); } // a1-a2, b1-b2
bool isPointOnLine(C a, C b, C c) { return isZero(det(b - a, c - a)); } // a-b <- c
/*
bool isPointOnLineSegment(C a, C b, C c) { // a-b <- c
  return isZero(det(b - a, c - a)) && isUEZero(dot(b - a, c - a)) && isUEZero(dot(a - b, c - b));
}
*/
bool isPointOnLineSegment(C a, C b, C c) { return isZero(abs(a-c) + abs(c-b) - abs(a-b)); }
double distanceLineAndPoint(C a, C b, C c) { return abs(det(b-a, c-a)) / abs(b-a); } // a-b <- c
double distanceLineSegmentAndPoint(C a, C b, C c) { // a-b <- c
  if (isLEZero(dot(b-a, c-a))) return abs(c-a);
  if (isLEZero(dot(a-b, c-b))) return abs(c-b);
  return abs(det(b-a, c-a)) / abs(b-a);
}
bool isIntersectedLine(C a1, C a2, C b1, C b2) { // a1-a2, b1-b2
  return !isLineParallel(a1, a2, b1, b2);
}
C intersectionLine(C a1, C a2, C b1, C b2) { // isIntersectedLine-> true
  C a = a2 - a1, b = b2 - b1;
  return a1 + a * det(b, b1 - a1) / det(b, a);
}

/**** NG Words ****/
// cx cy P Q C
// Warning: EPS

/**** main function ****/

ll N, cn, s, t, c;
vector<ll> s1[30], t1[30];
priority_queue<ll, vector<ll>, greater<ll>> S, T;

int main() {
  scanf("%lld%lld", &N, &cn);
  for (ll i = 0; i < N; i++) scanf("%lld%lld%lld", &s, &t, &c), s1[c-1].push_back(s), t1[c-1].push_back(t);
  for (ll i = 0; i < cn; i++) sort(s1[i].begin(), s1[i].end()), sort(t1[i].begin(), t1[i].end());
  for (ll i = 0; i < cn; i++) {
    if (s1[i].size() == 0) continue;
    S.push(s1[i][0]);
    for (ll j = 1; j < s1[i].size(); j++) {
      if (s1[i][j] != t1[i][j-1]) {
        T.push(t1[i][j-1]);
        S.push(s1[i][j]);
      }
    }
    T.push(t1[i][t1[i].size() - 1]);
  }
  ll counter = 0, ans = 0;
  while (!T.empty()) {
    if (S.empty()) s = INF;
    else s = S.top();
    t = T.top();
    if (s > t) {
      counter--;
      T.pop();
    } else {
      counter++;
      S.pop();
    }
    ans = max(ans, counter);
  }
  printf("%lld\n", ans);
}