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30865번 - xor 쿼리 다국어

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2 초 1024 MB71504580.357%

문제

길이가 $N$인 정수 수열 $a=[a_1,a_2,\ldots ,a_N]$이 주어질 때, 다음 쿼리를 처리하는 프로그램을 작성하시오.

  • 1ドル$ $i$ $x$: $a_i$의 값을 $x$로 변경한다.
  • 2ドル$ $i$ $x$: 수열 $[a_1\oplus x,a_2\oplus x,\ldots ,a_N\oplus x]$에서 중복을 포함하여 $i$번째로 큰 값을 출력한다.

여기서 $a\oplus b$는 $a$와 $b$의 비트간 논리적 배타합(bitwise xor) 연산을 의미한다.

입력

첫 번째 줄에 수열 $a$의 길이 $N$이 주어진다. $(1\le N\le 100,円 000)$

두 번째 줄에 $N$개의 정수 $a_1,a_2,\ldots ,a_N$이 공백으로 구분되어 주어진다. $(0\le a_i\le 2^{31}-1)$

세 번째 줄에 쿼리의 수 $Q$가 주어진다. $(1\le Q\le 100,円 000)$

네 번째 줄부터 $Q$개의 줄에 걸쳐 쿼리가 주어진다. 2ドル$번 쿼리는 한 번 이상 주어진다. $(1\le i\le N;$ 0ドル\le x\le 2^{31}-1)$

출력

2ドル$번 쿼리에 대한 결괏값을 한 줄에 하나씩 출력한다.

제한

예제 입력 1

9
1 2 3 4 5 6 7 8 9
11
2 1 7
2 2 7
2 3 7
1 1 3
1 2 3
1 4 3
2 1 12
2 2 12
2 3 12
2 4 12
2 5 12

예제 출력 1

15
14
6
15
15
15
15
11

수열 $[1,2,3,4,5,6,7,8,9]$의 모든 원소와 7ドル$을 xor 연산한 수열은 $[6,5,4,3,2,1,0,15,14]$이다. 이 중 첫 번째로 큰 값은 15ドル,ドル 두 번째로 큰 값은 14ドル,ドル 세 번째로 큰 값은 6ドル$이다.

처음 주어진 수열에서 첫 번째, 두 번째, 네 번째 값을 3ドル$으로 변경한 수열은 $[3,3,3,3,5,6,7,8,9]$이다.

변경된 수열의 모든 원소와 12ドル$를 xor 연산한 수열은 $[15,15,15,15,9,10,11,4,5]$이다. 이 중 첫 번째, 두 번째, 세 번째, 네 번째, 다섯 번째로 큰 값은 각각 15,15,15,15,11ドル$이다.

힌트

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