Robot Return to Origin

A robot starts at the origin, \( (0,0) \), on a 2D plane. The robot is given a string \( S \) consisting of characters 'U', 'D', 'L', and 'R', where:

• 'U' moves the robot up (i.e., increases the \( y \) coordinate by 1).
• 'D' moves the robot down (i.e., decreases the \( y \) coordinate by 1).
• 'L' moves the robot left (i.e., decreases the \( x \) coordinate by 1).
• 'R' moves the robot right (i.e., increases the \( x \) coordinate by 1).

Your task is to determine if the robot returns to the origin \( (0,0) \) after executing all the moves provided in \( S \). If the robot ends up back at the origin, output YES; otherwise, output NO.

For example, if \( S = "UD" \), the robot moves up and then down, returning to \( (0,0) \), so the output should be YES.

inputFormat

The input consists of a single line containing a non-empty string \( S \). The string \( S \) is composed only of the characters 'U', 'D', 'L', and 'R'.

Input is provided via stdin.

outputFormat

Output a single line: YES if the robot returns to the origin \( (0,0) \) after executing the moves in \( S \), otherwise output NO.

Output should be printed to stdout.

UD

YES