Lanterns

### 题目描述 有 $n$ 个灯笼拍成一排，第 $i$ 个灯笼具有 $p_i$ 的亮度。每个灯笼要么朝向左，照亮左边编号为 $[i - p_i,i - 1]$ 的灯笼，要么朝向右，照亮右边编号为 $[i + 1, i + p_i]$ 的灯笼。 寻找一种方案，为所有的灯笼确定朝向，使得每一个灯笼被至少一个其他灯笼照亮。 ### 输入格式 第一行一个正整数表示数据组数 $t$。 每组数据包含两行。第一行为一个正整数 $n$，表示灯笼的个数。 第二行 $n$ 个整数 $p_i$，表示各个灯笼的亮度。 ### 输出格式 对于每组数据，如果存在方案，在第一行输出字符串 $\texttt{YES}$，并在下一行给出一个长度为 $n$ 的仅由 $\texttt L$ 和 $\texttt R$ 组成的字符串，描述灯笼的方向。多解输出任意解。无解输出 $\texttt{NO}$。 ### 数据范围 $1\le t \le 1\times 10^4$。对于每组数据，有 $2\le n\le 3\times 10^5,0\le p_i\le n$。同一个测试点内保证 $\sum n\le 3\times 10^5$。

There are $ n $ lanterns in a row. The lantern $ i $ is placed in position $ i $ and has power equal to $ p_i $ . Each lantern can be directed to illuminate either some lanterns to the left or some lanterns to the right. If the $ i $ -th lantern is turned to the left, it illuminates all such lanterns $ j $ that $ j \in [i - p_i, i - 1] $ . Similarly, if it is turned to the right, it illuminates all such lanterns $ j $ that $ j \in [i + 1, i + p_i] $ . Your goal is to choose a direction for each lantern so each lantern is illuminated by at least one other lantern, or report that it is impossible.

The first line contains one integer $ t $ ( $ 1 \le t \le 10000 $ ) — the number of test cases. Each test case consists of two lines. The first line contains one integer $ n $ ( $ 2 \le n \le 3 \cdot 10^5 $ ) — the number of lanterns. The second line contains $ n $ integers $ p_1, p_2, \dots, p_n $ ( $ 0 \le p_i \le n $ ) — the power of the $ i $ -th lantern. The sum of $ n $ over all test cases does not exceed $ 3 \cdot 10^5 $ .

For each test case, print the answer as follows: If it is possible to direct all lanterns so that each lantern is illuminated, print YES in the first line and a string of $ n $ characters L and/or R (the $ i $ -th character is L if the $ i $ -th lantern is turned to the left, otherwise this character is R) in the second line. If there are multiple answers, you may print any of them. If there is no answer, simply print NO for that test case.

4
8
0 0 3 1 1 1 1 2
2
1 1
2
2 2
2
0 1

YES
RRLLLLRL
YES
RL
YES
RL
NO