CF1415F.Cakes for Clones

You live on a number line. You are initially (at time moment $t = 0$) located at point $x = 0$. There are $n$ events of the following type: at time $t_i$ a small cake appears at coordinate $x_i$. To collect this cake, you have to be at this coordinate at this point, otherwise the cake spoils immediately. No two cakes appear at the same time and no two cakes appear at the same coordinate.

You can move with the speed of $1$ length unit per one time unit. Also, at any moment you can create a clone of yourself at the same point where you are located. The clone can't move, but it will collect the cakes appearing at this position for you. The clone disappears when you create another clone. If the new clone is created at time moment $t$, the old clone can collect the cakes that appear before or at the time moment $t$, and the new clone can collect the cakes that appear at or after time moment $t$.

Can you collect all the cakes (by yourself or with the help of clones)?

你生活在一条数轴上。在初始时刻（$t = 0$）你位于坐标 $x = 0$ 处。共有 $n$ 个事件，每个事件的形式为：在时刻 $t_i$，坐标 $x_i$ 处会出现一块小蛋糕。要收集这块蛋糕，你必须恰好在时刻 $t_i$ 到达坐标 $x_i$；否则蛋糕会立即变质。任意两个蛋糕不会在同一时刻出现，也不会出现在同一坐标处。

你的移动速度为每单位时间移动 1 个长度单位。此外，在任意时刻，你可以在自己当前所在位置创建一个自己的克隆体。该克隆体不能移动，但它能替你收集在该位置出现的蛋糕。当你创建一个新的克隆体时，旧的克隆体会立即消失。若新克隆体于时刻 $t$ 创建，则旧克隆体可收集所有出现时刻 $\le t$ 的、位于其所在位置的蛋糕；而新克隆体则可收集所有出现时刻 $\ge t$ 的、位于其所在位置的蛋糕。

你能否（通过自身或借助克隆体）收集全部蛋糕？

The first line contains a single integer $n$ ($1 \le n \le 5000$) — the number of cakes.

Each of the next $n$ lines contains two integers $t_i$ and $x_i$ ($1 \le t_i \le 10^9$, $-10^9 \le x_i \le 10^9$) — the time and coordinate of a cake's appearance.

All times are distinct and are given in increasing order, all the coordinates are distinct.

第一行包含一个整数 $n$（$1 \le n \le 5000$）—— 蛋糕的数量。

接下来的 $n$ 行，每行包含两个整数 $t_i$ 和 $x_i$（$1 \le t_i \le 10^9$，$-10^9 \le x_i \le 10^9$）—— 分别表示第 $i$ 个蛋糕出现的时间和坐标。

所有时间互不相同，且按递增顺序给出；所有坐标互不相同。

Print "YES" if you can collect all cakes, otherwise print "NO".

如果可以收集所有蛋糕，则输出 "YES"，否则输出 "NO"。

In the first example you should start moving towards $5$ right away, leaving a clone at position $1$ at time moment $1$, and collecting the cake at position $2$ at time moment $2$. At time moment $5$ you are at the position $5$ and collect a cake there, your clone collects the last cake at time moment $6$.

In the second example you have to leave a clone at position $0$ and start moving towards position $5$. At time moment $1$ the clone collects a cake. At time moment $2$ you should create a new clone at the current position $2$, it will collect the last cake in future. You will collect the second cake at position $5$.

In the third example there is no way to collect all cakes.

在第一个例子中，你应该立即开始向位置 $5$ 移动，在时刻 $1$ 于位置 $1$ 留下一个分身，并在时刻 $2$ 到达位置 $2$ 收集蛋糕。在时刻 $5$，你到达位置 $5$ 并收集那里的蛋糕，而你的分身则在时刻 $6$ 收集最后一个蛋糕。

在第二个例子中，你必须在位置 $0$ 留下一个分身，然后开始向位置 $5$ 移动。在时刻 $1$，该分身收集一个蛋糕。在时刻 $2$，你应在当前位置 $2$ 创建一个新的分身，它将在未来收集最后一个蛋糕。你则会在位置 $5$ 收集第二个蛋糕。

在第三个例子中，不存在收集所有蛋糕的方法。