Uolevi is creating a list of numbers. He is particularly interested in bitwise XORs of the numbers in his list. Sometimes Uolevi wonders if it is possible to form a given number as a bitwise XOR of one or more numbers in his list.

To help Uolevi, implement a data structure that maintains a list of numbers and supports the following operations:

1. Add a number to the list
2. Determine if it is possible to select one or more numbers in the list such that the bitwise XOR of the numbers is equal to a given number

Initially the list is empty.

Input

The first line contains an integer q, the number of queries. Next q lines each contain two integers t_i and x_i where t_i is the type of the query. If the type is 1, you should add x_i to the list. If the type is 2 you should determine if it is possible to form x_i.

Output

For each query of type 2, output YES if it is possible to select one or more numbers in the list whose bitwise XOR is equal to x_i, and otherwise output NO.

Constraints

• 1 \le q \le 5 \cdot 10^5
• 0 \le x_i < 2^{20}

Example

Input:

6
1 1
1 2
1 4
2 5
2 7
2 0

Output:

YES
YES
NO

Input:

5
2 5
1 3
2 1
1 6
2 5

Output:

NO
NO
YES