#abc291c. [abc291_c]LRUD Instructions 2

[abc291_c]LRUD Instructions 2

Problem Statement

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

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

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

    • (x+1,y)(x+1,y) if the ii-th character of SS is R;
    • (x1,y)(x-1,y) if the ii-th character of SS is L;
    • (x,y+1)(x,y+1) if the ii-th character of SS is U; and
    • (x,y1)(x,y-1) if the ii-th character of SS is D,

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

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

Constraints

  • 1leqNleq2times1051 \\leq N \\leq 2\\times 10^5
  • NN is an integer.
  • SS is a string of length NN consisting of R, L, U, and D.

Input

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

NN SS

Output

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


Sample Input 1

5
RLURU

Sample Output 1

Yes

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


Sample Input 2

20
URDDLLUUURRRDDDDLLLL

Sample Output 2

No