Permutation

Problem Description

There are $N$ knights, with initial attack powers $a_1, a_2, \dots, a_n$. Each knight also has a buff ability $b_i$.

For each knight, he will choose some other knight (not himself) and increase that knight's attack power by $b_i$.

Determine whether there exists a permutation of the knights such that, no matter how each knight chooses the target of his buff, the attack powers of the knights are non-increasing from left to right.

Input Format

The first line contains a positive integer $T$, the number of test cases.

For each test case, the first line contains a positive integer $N$, the number of knights.

Each of the next $N$ lines contains two integers: the $i$-th line contains $a_i$ and $b_i$, the initial attack power and buff ability of knight $i$.

Output Format

For each test case, if there exists a permutation of the knights satisfying the requirement, output Yes; otherwise output No.

Sample Input

3
2
15 25
10 5
3
7 0
7 3
10 0
3
10 10
20 20
30 30

Sample Output

Yes
Yes
No

Sample Explanation

For the first test case, since $N = 2$, the final attack powers must be $35$ and $20$. It is clearly possible.

For the second test case, we can arrange the knights as $10, 7, 7$, placing the knight with buff ability $3$ last. Then no matter how the knight with buff ability $3$ chooses, the requirement is satisfied.

For the third test case, it can be proven that no arrangement satisfies the requirement, so output No.

Constraints

For all data, $1 \le T \le 1000$, $2 \le N \le 100$, and $0 \le a_i, b_i \le 10^6$.