CF1148E.Earth Wind and Fire

There are $n$ stones arranged on an axis. Initially the $i$-th stone is located at the coordinate $s_i$. There may be more than one stone in a single place.

You can perform zero or more operations of the following type:

• take two stones with indices $i$ and $j$ so that $s_i \leq s_j$, choose an integer $d$ ($0 \leq 2 \cdot d \leq s_j - s_i$), and replace the coordinate $s_i$ with $(s_i + d)$ and replace coordinate $s_j$ with $(s_j - d)$. In other words, draw stones closer to each other.

You want to move the stones so that they are located at positions $t_1, t_2, \ldots, t_n$. The order of the stones is not important — you just want for the multiset of the stones resulting positions to be the same as the multiset of $t_1, t_2, \ldots, t_n$.

Detect whether it is possible to move the stones this way, and if yes, construct a way to do so. You don't need to minimize the number of moves.

有 $n$ 块石头排列在一条数轴上。初始时，第 $i$ 块石头位于坐标 $s_i$ 处。同一位置上可能有多块石头。

你可以执行零次或多次如下操作：

• 选取下标为 $i$ 和 $j$ 的两块石头，满足 $s_i \leq s_j$；再任选一个整数 $d$（满足 $0 \leq 2 \cdot d \leq s_j - s_i$），将 $s_i$ 替换为 $(s_i + d)$，同时将 $s_j$ 替换为 $(s_j - d)$。换言之，使这两块石头彼此靠近。

你的目标是将石头移动至位置 $t_1, t_2, \ldots, t_n$。石头的顺序无关紧要——你只需使得最终所有石头所在位置构成的多重集，与 $t_1, t_2, \ldots, t_n$ 构成的多重集完全相同。

请判断是否能通过上述操作实现该目标；若可以，请构造一种具体的操作方案。你无需最小化操作次数。

The first line contains a single integer $n$ ($1 \le n \le 3 \cdot 10^5$) – the number of stones.

The second line contains integers $s_1, s_2, \ldots, s_n$ ($1 \le s_i \le 10^9$) — the initial positions of the stones.

The second line contains integers $t_1, t_2, \ldots, t_n$ ($1 \le t_i \le 10^9$) — the target positions of the stones.

第一行包含一个整数 $n$（$1 \le n \le 3 \cdot 10^5$）——石头的数量。

第二行包含整数 $s_1, s_2, \ldots, s_n$（$1 \le s_i \le 10^9$）——石头的初始位置。

第三行包含整数 $t_1, t_2, \ldots, t_n$（$1 \le t_i \le 10^9$）——石头的目标位置。

If it is impossible to move the stones this way, print "NO".

Otherwise, on the first line print "YES", on the second line print the number of operations $m$ ($0 \le m \le 5 \cdot n$) required. You don't have to minimize the number of operations.

Then print $m$ lines, each containing integers $i, j, d$ ($1 \le i, j \le n$, $s_i \le s_j$, $0 \leq 2 \cdot d \leq s_j - s_i$), defining the operations.

One can show that if an answer exists, there is an answer requiring no more than $5 \cdot n$ operations.

如果无法以这种方式移动石子，则输出 "NO"。

否则，第一行输出 "YES"，第二行输出所需的操作次数 $m$（$0 \le m \le 5 \cdot n$）。你无需最小化操作次数。

然后输出 $m$ 行，每行包含三个整数 $i, j, d$（$1 \le i, j \le n$，$s_i \le s_j$，$0 \leq 2 \cdot d \leq s_j - s_i$），用于描述各次操作。

可以证明：若解存在，则必存在一个操作次数不超过 $5 \cdot n$ 的解。

Consider the first example.

• After the first move the locations of stones is $[2, 2, 6, 5, 9]$.
• After the second move the locations of stones is $[2, 3, 5, 5, 9]$.
• After the third move the locations of stones is $[2, 5, 5, 5, 7]$.
• After the last move the locations of stones is $[4, 5, 5, 5, 5]$.

考虑第一个例子。

• 第一次移动后，石子的位置为 $[2, 2, 6, 5, 9]$。
• 第二次移动后，石子的位置为 $[2, 3, 5, 5, 9]$。
• 第三次移动后，石子的位置为 $[2, 5, 5, 5, 7]$。
• 最后一次移动后，石子的位置为 $[4, 5, 5, 5, 5]$。