#909 Eagle

Statement

Statement language

You are given a string $S$ of length $N$ . The string consists of lowercase English letters.

You may perform the following operation any number of times.

Choose one occurrence of the contiguous substring eagle in the current string and delete it. The parts remaining before and after the deleted substring are concatenated.

Determine whether it is possible to delete every character of the string by performing the operations in an appropriate order.

Input

The input is given in the following format.

$N$ $S$

Output

Print YES if it is possible to delete every character of the string, and NO otherwise.

Constraints

$1 \le N \le 500\,000$ .
$S$ is a lowercase English string of length $N$ .

Samples

Sample 1

Input

10
eagleaglee

Output

YES

Sample 2

Input

5
eagel

Output

NO