XOR Circle

Snuke has N hats. The i-th hat has an integer a_i written on it.

There are N camels standing in a circle. Snuke will put one of his hats on each of these camels.

If there exists a way to distribute the hats to the camels such that the following condition is satisfied for every camel, print Yes; otherwise, print No.

• The bitwise XOR of the numbers written on the hats on both adjacent camels is equal to the number on the hat on itself.

What is XOR? The bitwise XOR x_1 \oplus x_2 \oplus \ldots \oplus x_n of n non-negative integers x_1, x_2, \ldots, x_n is defined as follows: - When x_1 \oplus x_2 \oplus \ldots \oplus x_n is written in base two, the digit in the 2^k's place (k \geq 0) is 1 if the number of integers among x_1, x_2, \ldots, x_n whose binary representations have 1 in the 2^k's place is odd, and 0 if that count is even. For example, 3 \oplus 5 = 6.

Constraints

• All values in input are integers.
• 3 \leq N \leq 10^{5}
• 0 \leq a_i \leq 10^{9}

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_{N}

Output

Print the answer.

Examples

Input

3 1 2 3

Output

Yes

Input

4 1 2 4 8

Output

No

inputFormat

input are integers.

• 3 \leq N \leq 10^{5}
• 0 \leq a_i \leq 10^{9}

Input

Input is given from Standard Input in the following format:

N a_1 a_2 \ldots a_{N}

outputFormat

Output

Print the answer.

Examples

Input

3 1 2 3

Output

Yes

Input

4 1 2 4 8

Output

No

样例

3
1 2 3

Yes