#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const int MAXN = 1e6 + 5;
int T, n, tot, ans, res;
int a[MAXN], l[MAXN], r[MAXN], d[MAXN], cnt[MAXN];
int main() {
  scanf("%d", &T);
  while (T--) {
    tot = ans = 0;
    res = -INF;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      scanf("%d%d", &l[i], &r[i]);
      a[++tot] = l[i];
      a[++tot] = r[i];
    }
    sort(a + 1, a + 1 + tot);
    tot = unique(a + 1, a + 1 + tot) - a - 1;
    for (int i = 1; i <= n; i++) {
      l[i] = lower_bound(a + 1, a + 1 + tot, l[i]) - a;
      r[i] = lower_bound(a + 1, a + 1 + tot, r[i]) - a;
      l[i] <<= 1;
      r[i] <<= 1;
      d[l[i]]++;
      d[r[i] + 1]--;
    }
    tot <<= 1;
    tot += 5;
    for (int i = 1; i <= tot; i++) d[i] += d[i - 1];
    for (int i = 1; i <= tot; i++) {
      if (d[i] > 0 && d[i + 1] == 0) ans++;
    }
    for (int i = 1; i <= tot; i++) {
      if (d[i] == 1 && d[i + 1] != 1) cnt[i]++;
    }
    for (int i = 1; i <= tot; i++) {
      if (d[i] == 1 && d[i - 1] != 1) cnt[i]++;
    }
    for (int i = 1; i <= tot; i++) cnt[i] += cnt[i - 1];
    for (int i = 1; i <= n; i++) {
      int tmp = (cnt[r[i]] - cnt[l[i] - 1]) / 2;
      tmp -= (d[l[i]] == 1) + (d[r[i]] == 1);
      res = max(res, tmp);
    }
    printf("%d\n", ans + res);
    for (int i = 0; i <= tot; i++) d[i] = cnt[i] = 0;
  }
  return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

There are n segments on a Ox axis [l_1, r_1], [l_2, r_2], ..., [l_n, r_n]. Segment [l, r] covers all points from l to r inclusive, so all x such that l ≤ x ≤ r.

Segments can be placed arbitrarily — be inside each other, coincide and so on. Segments can degenerate into points, that is l_i=r_i is possible.

Union of the set of segments is such a set of segments which covers exactly the same set of points as the original set. For example:

  * if n=3 and there are segments [3, 6], [100, 100], [5, 8] then their union is 2 segments: [3, 8] and [100, 100]; 
  * if n=5 and there are segments [1, 2], [2, 3], [4, 5], [4, 6], [6, 6] then their union is 2 segments: [1, 3] and [4, 6]. 



Obviously, a union is a set of pairwise non-intersecting segments.

You are asked to erase exactly one segment of the given n so that the number of segments in the union of the rest n-1 segments is maximum possible.

For example, if n=4 and there are segments [1, 4], [2, 3], [3, 6], [5, 7], then:

  * erasing the first segment will lead to [2, 3], [3, 6], [5, 7] remaining, which have 1 segment in their union; 
  * erasing the second segment will lead to [1, 4], [3, 6], [5, 7] remaining, which have 1 segment in their union; 
  * erasing the third segment will lead to [1, 4], [2, 3], [5, 7] remaining, which have 2 segments in their union; 
  * erasing the fourth segment will lead to [1, 4], [2, 3], [3, 6] remaining, which have 1 segment in their union. 



Thus, you are required to erase the third segment to get answer 2.

Write a program that will find the maximum number of segments in the union of n-1 segments if you erase any of the given n segments.

Note that if there are multiple equal segments in the given set, then you can erase only one of them anyway. So the set after erasing will have exactly n-1 segments.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases in the test. Then the descriptions of t test cases follow.

The first of each test case contains a single integer n (2 ≤ n ≤ 2⋅10^5) — the number of segments in the given set. Then n lines follow, each contains a description of a segment — a pair of integers l_i, r_i (-10^9 ≤ l_i ≤ r_i ≤ 10^9), where l_i and r_i are the coordinates of the left and right borders of the i-th segment, respectively.

The segments are given in an arbitrary order.

It is guaranteed that the sum of n over all test cases does not exceed 2⋅10^5.

Output

Print t integers — the answers to the t given test cases in the order of input. The answer is the maximum number of segments in the union of n-1 segments if you erase any of the given n segments.

Example

Input


3
4
1 4
2 3
3 6
5 7
3
5 5
5 5
5 5
6
3 3
1 1
5 5
1 5
2 2
4 4


Output


2
1
5

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int INF = 0x3f3f3f3f;
const int MAXN = 1e6 + 5;
int T, n, tot, ans, res;
int a[MAXN], l[MAXN], r[MAXN], d[MAXN], cnt[MAXN];
int main() {
  scanf("%d", &T);
  while (T--) {
    tot = ans = 0;
    res = -INF;
    scanf("%d", &n);
    for (int i = 1; i <= n; i++) {
      scanf("%d%d", &l[i], &r[i]);
      a[++tot] = l[i];
      a[++tot] = r[i];
    }
    sort(a + 1, a + 1 + tot);
    tot = unique(a + 1, a + 1 + tot) - a - 1;
    for (int i = 1; i <= n; i++) {
      l[i] = lower_bound(a + 1, a + 1 + tot, l[i]) - a;
      r[i] = lower_bound(a + 1, a + 1 + tot, r[i]) - a;
      l[i] <<= 1;
      r[i] <<= 1;
      d[l[i]]++;
      d[r[i] + 1]--;
    }
    tot <<= 1;
    tot += 5;
    for (int i = 1; i <= tot; i++) d[i] += d[i - 1];
    for (int i = 1; i <= tot; i++) {
      if (d[i] > 0 && d[i + 1] == 0) ans++;
    }
    for (int i = 1; i <= tot; i++) {
      if (d[i] == 1 && d[i + 1] != 1) cnt[i]++;
    }
    for (int i = 1; i <= tot; i++) {
      if (d[i] == 1 && d[i - 1] != 1) cnt[i]++;
    }
    for (int i = 1; i <= tot; i++) cnt[i] += cnt[i - 1];
    for (int i = 1; i <= n; i++) {
      int tmp = (cnt[r[i]] - cnt[l[i] - 1]) / 2;
      tmp -= (d[l[i]] == 1) + (d[r[i]] == 1);
      res = max(res, tmp);
    }
    printf("%d\n", ans + res);
    for (int i = 0; i <= tot; i++) d[i] = cnt[i] = 0;
  }
  return 0;
}

```