Choosing The Commander

题意翻译

有一个初始为空的可重集 $S$。现在有 $Q$ 次操作，每次操作有 $3$ 种类型，分别是： - $1,p_i$，把 $p_i$ 加入 $S$。 - $2,p_i$，将 $p_i$ 从 $S$ 中删除，保证在删除前 $p_i$ 已经在 $S$ 中。 - $3,p_i,l_i$，询问 $S$ 中有多少个数按位异或上 $p_i$ 的结果**小于** $l_i$。 **【输入格式】** 第一行一个整数 $Q$，后面 $Q$ 行每行如题所述 **保证删除操作一定合法** 翻译:@an_interesting_name

题目描述

As you might remember from the previous round, Vova is currently playing a strategic game known as Rage of Empires. Vova managed to build a large army, but forgot about the main person in the army - the commander. So he tries to hire a commander, and he wants to choose the person who will be respected by warriors. Each warrior is represented by his personality — an integer number $ p_{i} $ . Each commander has two characteristics — his personality $ p_{j} $ and leadership $ l_{j} $ (both are integer numbers). Warrior $ i $ respects commander $ j $ only if  ( is the bitwise excluding OR of $ x $ and $ y $ ). Initially Vova's army is empty. There are three different types of events that can happen with the army: - $ 1 p_{i} $ — one warrior with personality $ p_{i} $ joins Vova's army; - $ 2 p_{i} $ — one warrior with personality $ p_{i} $ leaves Vova's army; - $ 3 p_{i} l_{i} $ — Vova tries to hire a commander with personality $ p_{i} $ and leadership $ l_{i} $ . For each event of the third type Vova wants to know how many warriors (counting only those who joined the army and haven't left yet) respect the commander he tries to hire.

输入输出格式

输入格式

The first line contains one integer $ q $ ( $ 1<=q<=100000 $ ) — the number of events. Then $ q $ lines follow. Each line describes the event: - $ 1 p_{i} $ ( $ 1<=p_{i}<=10^{8} $ ) — one warrior with personality $ p_{i} $ joins Vova's army; - $ 2 p_{i} $ ( $ 1<=p_{i}<=10^{8} $ ) — one warrior with personality $ p_{i} $ leaves Vova's army (it is guaranteed that there is at least one such warrior in Vova's army by this moment); - $ 3 p_{i} l_{i} $ ( $ 1<=p_{i},l_{i}<=10^{8} $ ) — Vova tries to hire a commander with personality $ p_{i} $ and leadership $ l_{i} $ . There is at least one event of this type.

输出格式

For each event of the third type print one integer — the number of warriors who respect the commander Vova tries to hire in the event.

输入输出样例

输入样例 #1

5
1 3
1 4
3 6 3
2 4
3 6 3

输出样例 #1

1
0

说明

In the example the army consists of two warriors with personalities $ 3 $ and $ 4 $ after first two events. Then Vova tries to hire a commander with personality $ 6 $ and leadership $ 3 $ , and only one warrior respects him (, and $ 2&lt;3 $ , but , and $ 5>=3 $ ). Then warrior with personality $ 4 $ leaves, and when Vova tries to hire that commander again, there are no warriors who respect him.