#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;
using ull = uint64_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f64 = double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = double;
namespace io {
const int BUFSIZE = 1 << 20;
int isize, osize;
char ibuf[BUFSIZE + 10], obuf[BUFSIZE + 10];
char *is, *it, *os = obuf, *ot = obuf + BUFSIZE;
char getchar() {
  if (is == it) {
    is = ibuf;
    it = ibuf + fread(ibuf, 1, BUFSIZE, stdin);
    if (is == it) return EOF;
  }
  return *is++;
}
char getalpha() {
  char c = getchar();
  while (!isalpha(c)) c = getchar();
  return c;
}
void putchar(char c) {
  *os++ = c;
  if (os == ot) {
    fwrite(obuf, 1, BUFSIZE, stdout);
    os = obuf;
  }
}
int inp() {
  int x = 0, f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return -1;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
ll inp_ll() {
  ll x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar())
    if (ch == '-') f = 1;
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
template <class T>
bool read(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  return 1;
}
bool read(char* s) {
  char* t = s;
  char ch = getchar();
  for (; ch == ' ' || ch == '\n'; ch = getchar())
    ;
  for (; ch != ' ' && ch != '\n' && ch != EOF; ch = getchar()) *t++ = ch;
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool read(T& x, Args&... args) {
  return read(x) && read(args...);
}
template <class T>
bool readln(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  for (; ch != '\n' && ch != EOF; ch = getchar())
    ;
  return 1;
}
bool readln(char* s) {
  char* t = s;
  while (1) {
    char ch = getchar();
    if (ch == '\n' || ch == EOF) break;
    *t++ = ch;
  }
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool readln(T& x, Args&... args) {
  return read(x) && readln(args...);
}
template <class T>
void write(T x) {
  static char s[22];
  static char* it = s + 20;
  static char* end = s + 20;
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  do {
    *--it = x % 10 + '0';
    x /= 10;
  } while (x);
  for (; it < end; ++it) putchar(*it);
}
void write(const char* s) {
  for (; *s; ++s) putchar(*s);
}
template <>
void write(char* s) {
  write((const char*)s);
}
template <>
void write(char c) {
  putchar(c);
}
template <class T, class... Args>
void write(T x, Args... args) {
  write(x);
  write(args...);
}
void writeln() { putchar('\n'); }
template <class T, class... Args>
void writeln(T x, Args... args) {
  write(x);
  writeln(args...);
}
template <class Iterator>
bool input(Iterator st, Iterator ed) {
  for (; st != ed; ++st) {
    if (!read(*st)) return false;
  }
  return true;
}
template <class T>
bool input(T& a) {
  return input(a.begin(), a.end());
}
template <class Iterator>
void print(Iterator st, Iterator ed, const char* c = " ") {
  int flag = 0;
  for (; st != ed; ++st) {
    if (flag) write(c);
    flag = 1;
    write(*st);
  }
  writeln();
}
template <class T>
void print(const T& a, const char* c = " ") {
  print(a.begin(), a.end(), c);
}
struct ender {
  ~ender() {
    if (os != obuf) fwrite(obuf, 1, os - obuf, stdout);
  }
} __ender;
}  // namespace io
int64_t power(int64_t a, int64_t b, int64_t p) {
  if (!b) return 1;
  int64_t t = power(a, b >> 1, p);
  t = t * t % p;
  if (b & 1) t = t * a % p;
  return t;
}
pll exgcd(ll a, ll b) {
  if (b == 0) return {1, 0};
  auto e = exgcd(b, a % b);
  ll x = e.first;
  ll y = e.second;
  return {y, x - a / b * y};
}
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
using namespace io;
template <class T>
inline void freshmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
inline void freshmax(T& a, const T& b) {
  if (a < b) a = b;
}
int dx[] = {-1, 1, 0, 0, -1, -1, 1, 1};
int dy[] = {0, 0, -1, 1, -1, 1, -1, 1};
template <class T>
T det(T x1, T y1, T x2, T y2, T x3, T y3) {
  return x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3;
}
template <class T>
T dis(T x1, T y1, T x2, T y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
void init() {}
const int MAXN = 6010;
int x[MAXN], y[MAXN];
bool has[MAXN][MAXN];
int f[MAXN][MAXN];
void solve() {
  int n;
  read(n);
  vector<int> p;
  for (int i = 0; i < n; ++i) {
    read(x[i], y[i]);
    p.push_back(x[i]);
    p.push_back(y[i]);
  }
  sort(p.begin(), p.end());
  p.erase(unique(p.begin(), p.end()), p.end());
  int m = p.size();
  for (int i = 1; i <= m; ++i)
    for (int j = 1; j <= m; ++j) has[i][j] = 0;
  vector<vector<int>> v(m + 1);
  for (int i = 0; i < n; ++i) {
    x[i] = lower_bound(p.begin(), p.end(), x[i]) - p.begin() + 1;
    y[i] = lower_bound(p.begin(), p.end(), y[i]) - p.begin() + 1;
    has[x[i]][y[i]] = 1;
    v[x[i]].push_back(y[i]);
  }
  for (int i = 1; i <= m; ++i) f[i][i] = has[i][i];
  for (int i = m; i >= 1; --i)
    for (int j = i + 1; j <= m; ++j) {
      f[i][j] = max(f[i][j - 1], f[i + 1][j]);
      for (int k : v[i]) {
        if (k < j) freshmax(f[i][j], f[i][k] + f[k + 1][j]);
      }
      f[i][j] += has[i][j];
    }
  writeln(f[1][m]);
}
int main() {
  int T = 1;
  read(T);
  init();
  for (int test = 1; test <= T; ++test) {
    solve();
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

You are given n segments on a coordinate axis OX. The i-th segment has borders [l_i; r_i]. All points x, for which l_i ≤ x ≤ r_i holds, belong to the i-th segment.

Your task is to choose the maximum by size (the number of segments) subset of the given set of segments such that each pair of segments in this subset either non-intersecting or one of them lies inside the other one.

Two segments [l_i; r_i] and [l_j; r_j] are non-intersecting if they have no common points. For example, segments [1; 2] and [3; 4], [1; 3] and [5; 5] are non-intersecting, while segments [1; 2] and [2; 3], [1; 2] and [2; 2] are intersecting.

The segment [l_i; r_i] lies inside the segment [l_j; r_j] if l_j ≤ l_i and r_i ≤ r_j. For example, segments [2; 2], [2, 3], [3; 4] and [2; 4] lie inside the segment [2; 4], while [2; 5] and [1; 4] are not.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.

The first line of the test case contains one integer n (1 ≤ n ≤ 3000) — the number of segments. The next n lines describe segments. The i-th segment is given as two integers l_i and r_i (1 ≤ l_i ≤ r_i ≤ 2 ⋅ 10^5), where l_i is the left border of the i-th segment and r_i is the right border of the i-th segment.

Additional constraint on the input: there are no duplicates in the list of segments.

It is guaranteed that the sum of n does not exceed 3000 (∑ n ≤ 3000).

Output

For each test case, print the answer: the maximum possible size of the subset of the given set of segments such that each pair of segments in this subset either non-intersecting or one of them lies inside the other one.

Example

Input


4
4
1 5
2 4
2 3
3 4
5
1 5
2 3
2 5
3 5
2 2
3
1 3
2 4
2 3
7
1 10
2 8
2 5
3 4
4 4
6 8
7 7


Output


3
4
2
7

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = int64_t;
using ull = uint64_t;
using i32 = int32_t;
using u32 = uint32_t;
using i64 = int64_t;
using u64 = uint64_t;
using f64 = double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = double;
namespace io {
const int BUFSIZE = 1 << 20;
int isize, osize;
char ibuf[BUFSIZE + 10], obuf[BUFSIZE + 10];
char *is, *it, *os = obuf, *ot = obuf + BUFSIZE;
char getchar() {
  if (is == it) {
    is = ibuf;
    it = ibuf + fread(ibuf, 1, BUFSIZE, stdin);
    if (is == it) return EOF;
  }
  return *is++;
}
char getalpha() {
  char c = getchar();
  while (!isalpha(c)) c = getchar();
  return c;
}
void putchar(char c) {
  *os++ = c;
  if (os == ot) {
    fwrite(obuf, 1, BUFSIZE, stdout);
    os = obuf;
  }
}
int inp() {
  int x = 0, f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return -1;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
ll inp_ll() {
  ll x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar())
    if (ch == '-') f = 1;
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  return f ? -x : x;
}
template <class T>
bool read(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  return 1;
}
bool read(char* s) {
  char* t = s;
  char ch = getchar();
  for (; ch == ' ' || ch == '\n'; ch = getchar())
    ;
  for (; ch != ' ' && ch != '\n' && ch != EOF; ch = getchar()) *t++ = ch;
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool read(T& x, Args&... args) {
  return read(x) && read(args...);
}
template <class T>
bool readln(T& x) {
  x = 0;
  int f = 0;
  char ch;
  for (ch = getchar(); !isdigit(ch); ch = getchar()) {
    if (ch == EOF) return 0;
    if (ch == '-') f = 1;
  }
  for (; isdigit(ch); x = x * 10 + ch - '0', ch = getchar())
    ;
  if (f) x = -x;
  for (; ch != '\n' && ch != EOF; ch = getchar())
    ;
  return 1;
}
bool readln(char* s) {
  char* t = s;
  while (1) {
    char ch = getchar();
    if (ch == '\n' || ch == EOF) break;
    *t++ = ch;
  }
  *t = 0;
  return s != t;
}
template <class T, class... Args>
bool readln(T& x, Args&... args) {
  return read(x) && readln(args...);
}
template <class T>
void write(T x) {
  static char s[22];
  static char* it = s + 20;
  static char* end = s + 20;
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  do {
    *--it = x % 10 + '0';
    x /= 10;
  } while (x);
  for (; it < end; ++it) putchar(*it);
}
void write(const char* s) {
  for (; *s; ++s) putchar(*s);
}
template <>
void write(char* s) {
  write((const char*)s);
}
template <>
void write(char c) {
  putchar(c);
}
template <class T, class... Args>
void write(T x, Args... args) {
  write(x);
  write(args...);
}
void writeln() { putchar('\n'); }
template <class T, class... Args>
void writeln(T x, Args... args) {
  write(x);
  writeln(args...);
}
template <class Iterator>
bool input(Iterator st, Iterator ed) {
  for (; st != ed; ++st) {
    if (!read(*st)) return false;
  }
  return true;
}
template <class T>
bool input(T& a) {
  return input(a.begin(), a.end());
}
template <class Iterator>
void print(Iterator st, Iterator ed, const char* c = " ") {
  int flag = 0;
  for (; st != ed; ++st) {
    if (flag) write(c);
    flag = 1;
    write(*st);
  }
  writeln();
}
template <class T>
void print(const T& a, const char* c = " ") {
  print(a.begin(), a.end(), c);
}
struct ender {
  ~ender() {
    if (os != obuf) fwrite(obuf, 1, os - obuf, stdout);
  }
} __ender;
}  // namespace io
int64_t power(int64_t a, int64_t b, int64_t p) {
  if (!b) return 1;
  int64_t t = power(a, b >> 1, p);
  t = t * t % p;
  if (b & 1) t = t * a % p;
  return t;
}
pll exgcd(ll a, ll b) {
  if (b == 0) return {1, 0};
  auto e = exgcd(b, a % b);
  ll x = e.first;
  ll y = e.second;
  return {y, x - a / b * y};
}
mt19937 rd(chrono::steady_clock::now().time_since_epoch().count());
using namespace io;
template <class T>
inline void freshmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
inline void freshmax(T& a, const T& b) {
  if (a < b) a = b;
}
int dx[] = {-1, 1, 0, 0, -1, -1, 1, 1};
int dy[] = {0, 0, -1, 1, -1, 1, -1, 1};
template <class T>
T det(T x1, T y1, T x2, T y2, T x3, T y3) {
  return x1 * y2 - x2 * y1 + x2 * y3 - x3 * y2 + x3 * y1 - x1 * y3;
}
template <class T>
T dis(T x1, T y1, T x2, T y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
void init() {}
const int MAXN = 6010;
int x[MAXN], y[MAXN];
bool has[MAXN][MAXN];
int f[MAXN][MAXN];
void solve() {
  int n;
  read(n);
  vector<int> p;
  for (int i = 0; i < n; ++i) {
    read(x[i], y[i]);
    p.push_back(x[i]);
    p.push_back(y[i]);
  }
  sort(p.begin(), p.end());
  p.erase(unique(p.begin(), p.end()), p.end());
  int m = p.size();
  for (int i = 1; i <= m; ++i)
    for (int j = 1; j <= m; ++j) has[i][j] = 0;
  vector<vector<int>> v(m + 1);
  for (int i = 0; i < n; ++i) {
    x[i] = lower_bound(p.begin(), p.end(), x[i]) - p.begin() + 1;
    y[i] = lower_bound(p.begin(), p.end(), y[i]) - p.begin() + 1;
    has[x[i]][y[i]] = 1;
    v[x[i]].push_back(y[i]);
  }
  for (int i = 1; i <= m; ++i) f[i][i] = has[i][i];
  for (int i = m; i >= 1; --i)
    for (int j = i + 1; j <= m; ++j) {
      f[i][j] = max(f[i][j - 1], f[i + 1][j]);
      for (int k : v[i]) {
        if (k < j) freshmax(f[i][j], f[i][k] + f[k + 1][j]);
      }
      f[i][j] += has[i][j];
    }
  writeln(f[1][m]);
}
int main() {
  int T = 1;
  read(T);
  init();
  for (int test = 1; test <= T; ++test) {
    solve();
  }
  return 0;
}

```