Nice Party

Problem Description

cc is going to throw a party and invites his friends so that everyone has a good time.

cc has $n$ friends; the $i$-th friend has net worth $i$.

The $i$-th friend will attend the party and enjoy it if and only if there are at most $X_i$ people present whose net worth is strictly greater than his, and at most $Y_i$ people whose net worth is strictly smaller than his.

cc wants to know: what is the maximum number of friends he can invite such that every invited friend enjoys the party?

Input Format

The first line gives an integer $T$, the number of test cases ($1 \le T \le 10^4$).

For each test case:

• The first line gives an integer $n$ ($1 \le \sum n \le 2 \times 10^5$), the number of friends.
• The following $n$ lines each give two integers $X_i$ and $Y_i$ ($0 \le X_i, Y_i < n$).

Output Format

For each test case, output one integer: the maximum number of friends cc can invite.

Sample Input

3
3
1 2
2 1
1 1
2
0 0
0 1
2
1 0
0 1

Sample Output

2
1
2