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C - LRUD Instructions 2

Score : $300$ points

Problem Statement

Takahashi is on a two-dimensional plane. Starting from the origin, he made $N$ moves.

The $N$ moves are represented by a string of length $N$ as described below:

• Takahashi's coordinates after the $i$-th move are:

  • $(x+1,y)$ if the $i$-th character of $S$ is R;
  • $(x-1,y)$ if the $i$-th character of $S$ is L;
  • $(x,y+1)$ if the $i$-th character of $S$ is U; and
  • $(x,y-1)$ if the $i$-th character of $S$ is D,

  where $(x,y)$ is his coordinates before the move.

Determine if Takahashi visited the same coordinates multiple times in the course of the $N$ moves (including the starting and ending points).

Constraints

• $1 \leq N \leq 2\times 10^5$
• $N$ is an integer.
• $S$ is a string of length $N$ consisting of R, L, U, and D.

Input

The input is given from Standard Input in the following format:

$N$

$S$

Output

Print Yes if Takahashi visited the same coordinates multiple times in the course of the $N$ moves; print No otherwise.

5
RLURU

Yes

Takahashi's coordinates change as follows: $(0,0)\to (1,0)\to (0,0)\to (0,1)\to (1,1)\to (1,2)$.

20
URDDLLUUURRRDDDDLLLL

No