A group of CS freshmen are experimenting with code snippets in the kiosk's text editor, and Rina needs the editor to flag whether their parentheses are properly balanced before they try to compile anything. Read a string made only of characters '(' and ')'. Print "YES" if the brackets are balanced (every open has a matching close, and never more closes than opens at any prefix), otherwise "NO".
Input
One string S of '(' and ')'.
Output
"YES" or "NO".
Constraints
1 ≤ |S| ≤ 10^5
Sample Input
(()())
Sample Output
YES
main.c
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