Distinct or Not

Given is a sequence of integers A_1, A_2, ..., A_N. If its elements are pairwise distinct, print YES; otherwise, print NO.

Constraints

• 2 ≤ N ≤ 200000
• 1 ≤ A_i ≤ 10^9
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 ... A_N

Output

If the elements of the sequence are pairwise distinct, print YES; otherwise, print NO.

Examples

Input

5 2 6 1 4 5

Output

YES

Input

6 4 1 3 1 6 2

Output

NO

Input

2 10000000 10000000

Output

NO

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 ... A_N

outputFormat

Output

If the elements of the sequence are pairwise distinct, print YES; otherwise, print NO.

Examples

Input

5 2 6 1 4 5

Output

YES

Input

6 4 1 3 1 6 2

Output

NO

Input

2 10000000 10000000

Output

NO

样例

6
4 1 3 1 6 2

NO