Attack Order

In a certain game, you control a board of $n$ minions numbered from $1$ to $n$. Each minion $i$ has an integer $a\_i$, called its attack.

For the upcoming fight, you arrange the minions in a line from left to right.

After that, some of the minions' attacks get buffed. The ability of each minion $i$ reads "Before the fight, increase the attack of another random minion by $b\_i$". Formally, for each $i$, an arbitrary minion $j \ne i$ is chosen and its attack $a\_j$ is increased by $b\_i$.

The buff targets are chosen independently and the buffs happen simultaneously. In particular, the attack of any minion can get buffed multiple times.

You want the attacks of the minions to be non-increasing from left to right after all the buffs happen. Determine whether it is possible to arrange the minions so that this holds regardless of how the buff targets are chosen.

Each input contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The test cases follow.

The first line of each test case contains a single integer $n$ ($2 \le n \le 100$).

The $i$-th of the next $n$ lines contains two integers $a\_i$ and $b\_i$ ($0 \le a\_i, b\_i \le 10^6$).

For each test case, print "Yes" if it is possible to arrange the minions so that their attacks are non-increasing regardless of how the buff targets are chosen, and "No" otherwise.

In the first example, the minions buff each other. The attacks of minions $1$ and $2$ during the fight are always $20$ and $35$, respectively. You can arrange the minions in the order $\langle 2, 1 \rangle$.

In the second example, only minion $2$ buffs another minion. One valid ordering is $\langle 3, 1, 2 \rangle$. If minion $2$ buffs minion $1$, the attacks of the minions, from left to right, are $\langle 10, 10, 7 \rangle$. If minion $2$ buffs minion $3$, the attacks are $\langle 13, 7, 7 \rangle$. Both sequences are non-increasing.