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Contest: Task: Related: TaskD TaskF

Score : $500$ points

Problem Statement

Solve the following problem for $T$ test cases.

There are $10^9$ boxes numbered $1,2,\dots,10^9$ and $N$ balls numbered $1,2,\dots,N$.
Each box can contain at most one ball.
Determine whether it is possible to put all $N$ balls in the boxes so that the following condition will be satisfied.

  • For each integer $i$ from $1$ through $N$, the ball numbered $i$ is in a box numbered between $L_i$ and $R_i$ (inclusive).

Constraints

  • $1 \le T \le 2 \times 10^5$
  • $1 \le N \le 2 \times 10^5$
  • $1 \le L_i \le R_i \le 10^9$
  • The sum of $N$ across the test cases in one input is at most $2 \times 10^5$.

Input

Input is given from Standard Input. The first line is in the following format:

$T$

Then, $T$ test cases follows, each of which is in the following format:

$N$
$L_1$ $R_1$
$L_2$ $R_2$
$\dots$
$L_N$ $R_N$

Output

Your output should have $T$ lines.
In the $i$-th $(1 \le i \le T)$ line, print Yes if it is possible to put all $N$ balls in the boxes so that the condition will be satisfied in the $i$-th test case in the input, and printNo otherwise.
The checker is case-insensitive; it will accept both uppercase and lowercase letters.

Sample Input 1

2
3
1 2
2 3
3 3
5
1 2
2 3
3 3
1 3
999999999 1000000000

Sample Output 1

Yes
No

This input contains two test cases.

  • In the $1$-st test case, the following way to put the three balls would satisfy the condition, so we should print Yes.

    • Put Ball $1$ in Box $1$.
    • Put Ball $2$ in Box $2$.
    • Put Ball $3$ in Box $3$.

  • In the $2$-nd test case, there is no way to put the five balls to satisfy the condition, so we should print No.