K. Rain on Birthday
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You have been competing at UTPC since about 6 PM, and you realized that you need to rush to a birthday party immediately after! You peek outside, and you see that it has been raining acid! You don't want to get harmed, so you decide to construct some umbrellas.

You quickly run to Welch and start searching for chemicals. Suppose you currently are in possession of a set of chemicals. Each chemical can be described by some positive integer $$$c$$$. To create new chemical for the umbrella, you can pick a subset of the chemicals you have and compute the bitwise XOR of the subset, which describes the new chemical. If your set of chemicals is empty, the new chemical you create is just 0.

Any chemical you create can be used to construct an umbrella. Acids can also be described by a positive integer. Some chemical $$$c$$$ can protect against acid $$$a$$$ with protection level $$$b$$$ if $$$c \& a = b$$$, where $$$\&$$$ is bitwise AND.

You are given multiple queries, where you either add a new chemical to your overall set or check if you can create a chemical that can protect against the acid. Figure out what acids you can protect against for each query!

Input

The first line contains $$$q$$$ ($$$1 \leq q \leq 10^5$$$) — the number of queries. The following $$$q$$$ lines contain either of the following two inputs:

  • $$$1\ c$$$: Add $$$c$$$ to the set of possible chemicals ($$$0 \leq c \lt 2^{30}$$$).
  • $$$2\ a\ b$$$: Check if you can construct some chemical $$$c$$$ where $$$c \& a = b$$$ ($$$0 \leq a, b, \lt 2^{30}$$$).
Output

For each query of type 2, print "YES" if you can construct some chemical $$$c$$$ where $$$c \& a = b$$$, and "NO" otherwise. Each answer should be on its own line.

Example
Input
8
1 3
2 3 2
2 2 2
1 1
2 3 2
2 2 2
2 0 2
2 1073741823 0
Output
NO
YES
YES
YES
NO
YES