문제
민찬이는 KSA 학생들을 위해 1ドル$번부터 $N$번까지의 문제들로 구성된 문제 목록을 준비했다. $i$번 문제의 레벨은 $A_i$이다.
학생들로부터 문제가 너무 많다는 불평을 들은 민찬이는 문제 목록을 한 개 이상의 연속된 구간으로 분할해, 구간마다 그 구간에 속한 문제들을 하나의 새로운 문제로 대체하려고 한다. 단, 각 구간에는 적어도 하나의 문제가 포함되어 있어야 하며, KSA 학생들을 더 헷갈리게 하기 위해 인접한 두 구간의 문제 수는 서로 다르도록 분할해야 한다.
새로운 문제의 레벨은 해당하는 구간에 속한 문제의 레벨을 모두 bitwise XOR한 값이다. 민찬이는 KSA 학생들의 실력 향상을 위해 새로운 문제들의 레벨 합을 최대로 하려고 한다. 문제 목록을 적절한 구간들로 분할했을 때, 새로운 문제들의 레벨 합의 최댓값을 구해보자.
출력
새로운 문제들의 레벨 합의 최댓값을 출력한다.
제한
- 1ドル \leq N \leq 2 \times 10^5$
- 0ドル \leq A_i \leq 10^9$ $(1 \leq i \leq N)$
서브태스크
| 번호 | 배점 | 제한 | | 1 | 23 | $N \le 100$
|
| 2 | 36 | $N \le 3000$
|
| 3 | 41 | 추가 제약 조건 없음
|
$[1, 2],ドル $[3, 3]$ 두 구간으로 분할하면 레벨 합을 8ドル$로 만들 수 있다.
$(5 \oplus 3) + (2) = 8$
$[1, 1],ドル $[2, 3],ドル $[4, 4]$ 세 구간으로 분할하면 레벨 합을 18ドル$로 만들 수 있다.
$(6) + (2 \oplus 4) + (6) = 18$
$[1, 4]$ 한 구간으로 분할하면 레벨 합을 15ドル$로 만들 수 있다.
$(1 \oplus 2 \oplus 4 \oplus 8)= 15$
노트
음이 아닌 두 정수 $A$와 $B$의 bitwise XOR, 즉 $A \oplus B$는 다음과 같이 정의된다:
- $A \oplus B$를 이진수로 나타냈을때 2ドル^k$의 자리 숫자($k \geq 0$)는 $A$와 $B$에서 그 자리에 있는 숫자 중 정확히 하나가 1ドル$이면 1ドル$이고, 그렇지 않다면 0ドル$이다.
예를 들어, 3ドル \oplus 5 = 6$이다. (이진수로 나타내면: 011ドル \oplus 101 = 110$).
[{"problem_id":"29200","problem_lang":"0","title":"\ubb38\uc81c \uc218 \uc904\uc774\uae30","description":"<p>\ubbfc\ucc2c\uc774\ub294 KSA \ud559\uc0dd\ub4e4\uc744 \uc704\ud574 $1$\ubc88\ubd80\ud130 $N$\ubc88\uae4c\uc9c0\uc758 \ubb38\uc81c\ub4e4\ub85c \uad6c\uc131\ub41c \ubb38\uc81c \ubaa9\ub85d\uc744 \uc900\ube44\ud588\ub2e4. $i$\ubc88 \ubb38\uc81c\uc758 \ub808\ubca8\uc740 $A_i$\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud559\uc0dd\ub4e4\ub85c\ubd80\ud130 \ubb38\uc81c\uac00 \ub108\ubb34 \ub9ce\ub2e4\ub294 \ubd88\ud3c9\uc744 \ub4e4\uc740 \ubbfc\ucc2c\uc774\ub294 \ubb38\uc81c \ubaa9\ub85d\uc744 \ud55c \uac1c \uc774\uc0c1\uc758 \uc5f0\uc18d\ub41c \uad6c\uac04\uc73c\ub85c \ubd84\ud560\ud574, \uad6c\uac04\ub9c8\ub2e4 \uadf8 \uad6c\uac04\uc5d0 \uc18d\ud55c \ubb38\uc81c\ub4e4\uc744 \ud558\ub098\uc758 \uc0c8\ub85c\uc6b4 \ubb38\uc81c\ub85c \ub300\uccb4\ud558\ub824\uace0 \ud55c\ub2e4. \ub2e8, \uac01 \uad6c\uac04\uc5d0\ub294 \uc801\uc5b4\ub3c4 \ud558\ub098\uc758 \ubb38\uc81c\uac00 \ud3ec\ud568\ub418\uc5b4 \uc788\uc5b4\uc57c \ud558\uba70, KSA \ud559\uc0dd\ub4e4\uc744 \ub354 \ud5f7\uac08\ub9ac\uac8c \ud558\uae30 \uc704\ud574 \uc778\uc811\ud55c \ub450 \uad6c\uac04\uc758 \ubb38\uc81c \uc218\ub294 \uc11c\ub85c \ub2e4\ub974\ub3c4\ub85d \ubd84\ud560\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc0c8\ub85c\uc6b4 \ubb38\uc81c\uc758 \ub808\ubca8\uc740 \ud574\ub2f9\ud558\ub294 \uad6c\uac04\uc5d0 \uc18d\ud55c \ubb38\uc81c\uc758 \ub808\ubca8\uc744 \ubaa8\ub450 bitwise XOR\ud55c \uac12\uc774\ub2e4. \ubbfc\ucc2c\uc774\ub294 KSA \ud559\uc0dd\ub4e4\uc758 \uc2e4\ub825 \ud5a5\uc0c1\uc744 \uc704\ud574 \uc0c8\ub85c\uc6b4 \ubb38\uc81c\ub4e4\uc758 \ub808\ubca8 \ud569\uc744 \ucd5c\ub300\ub85c \ud558\ub824\uace0 \ud55c\ub2e4. \ubb38\uc81c \ubaa9\ub85d\uc744 \uc801\uc808\ud55c \uad6c\uac04\ub4e4\ub85c \ubd84\ud560\ud588\uc744 \ub54c, \uc0c8\ub85c\uc6b4 \ubb38\uc81c\ub4e4\uc758 \ub808\ubca8 \ud569\uc758 \ucd5c\ub313\uac12\uc744 \uad6c\ud574\ubcf4\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 $N$\uac1c\uc758 \uc815\uc218 $A_1, A_2, \\cdots, A_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uc0c8\ub85c\uc6b4 \ubb38\uc81c\ub4e4\uc758 \ub808\ubca8 \ud569\uc758 \ucd5c\ub313\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc74c\uc774 \uc544\ub2cc \ub450 \uc815\uc218 $A$\uc640 $B$\uc758 bitwise XOR, \uc989 $A \\oplus B$\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ub41c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>$A \\oplus B$\ub97c \uc774\uc9c4\uc218\ub85c \ub098\ud0c0\ub0c8\uc744\ub54c $2^k$\uc758 \uc790\ub9ac \uc22b\uc790($k \\geq 0$)\ub294 $A$\uc640 $B$\uc5d0\uc11c \uadf8 \uc790\ub9ac\uc5d0 \uc788\ub294 \uc22b\uc790 \uc911 \uc815\ud655\ud788 \ud558\ub098\uac00 $1$\uc774\uba74 $1$\uc774\uace0, \uadf8\ub807\uc9c0 \uc54a\ub2e4\uba74 $0$\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, $3 \\oplus 5 = 6$\uc774\ub2e4. (\uc774\uc9c4\uc218\ub85c \ub098\ud0c0\ub0b4\uba74: $011 \\oplus 101 = 110$).<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1 \\leq N \\leq 2 \\times 10^5$<\/li>\r\n\t<li>$0 \\leq A_i \\leq 10^9$ $(1 \\leq i \\leq N)$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 100$<\/p>\r\n","subtask2":"<p>$N \\le 3000$<\/p>\r\n","subtask3":"<p>\ucd94\uac00 \uc81c\uc57d \uc870\uac74 \uc5c6\uc74c<\/p>\r\n","sample_explain_1":"<p>$[1, 2]$, $[3, 3]$ \ub450 \uad6c\uac04\uc73c\ub85c \ubd84\ud560\ud558\uba74 \ub808\ubca8 \ud569\uc744 $8$\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>$(5 \\oplus 3) + (2) = 8$<\/p>\r\n","sample_explain_2":"<p>$[1, 1]$, $[2, 3]$, $[4, 4]$ \uc138&nbsp;\uad6c\uac04\uc73c\ub85c \ubd84\ud560\ud558\uba74 \ub808\ubca8 \ud569\uc744 $18$\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>$(6) + (2 \\oplus 4) + (6) = 18$<\/p>\r\n","sample_explain_3":"<p>$[1, 4]$ \ud55c&nbsp;\uad6c\uac04\uc73c\ub85c \ubd84\ud560\ud558\uba74 \ub808\ubca8 \ud569\uc744 $15$\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>$(1 \\oplus 2 \\oplus 4 \\oplus 8)= 15$<\/p>\r\n"},{"problem_id":"29200","problem_lang":"1","title":"Reducing the Number of Problems","description":"<p>Minchan has prepared a list of problems for KSA students, consisting of problems numbered from $1$ to $N$. The level of problem $i$ is $A_i$.<\/p>\r\n\r\n<p>After receiving complaints from the students about having too many problems, Minchan wants to divide the problem list into one or more consecutive segments and replace each segment with a new problem. However, each segment must contain at least one problem, and adjacent segments must have different numbers of problems to confuse the KSA students.<\/p>\r\n\r\n<p>The level of the new problem is the bitwise XOR of the levels of the problems in the corresponding segment. Minchan wants to maximize the sum of the levels of the new problems for the improvement of the KSA students&#39; skills. Let&#39;s find the maximum possible sum of the levels of the new problems when dividing the problem list into appropriate segments.<\/p>\r\n","input":"<p>The first line contains an integer $N$.<\/p>\r\n\r\n<p>The second line contains $N$ space-separated integers $A_1, A_2, \\cdots, A_N$.<\/p>\r\n","output":"<p>Print the maximum possible sum of the levels of the new problems.<\/p>\r\n","hint":"<p>The bitwise XOR of non-negative integers $A$ and $B$, $A \\oplus B$, is defined as follows:<\/p>\r\n\r\n<ul>\r\n\t<li>When $A \\oplus B$ is written in base two, the digit in the $2^k$&#39;s place$(k \\geq 0)$ is 1 if exactly one of the digits in that place of $A$ and $B$ is $1$, and $0$ otherwise<\/li>\r\n<\/ul>\r\n\r\n<p>For example, we have $3 \\oplus 5 = 6$ (in base two: $011 \\oplus 101 = 110$).&nbsp;<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1 \\leq N \\leq 2 \\times 10^5$<\/li>\r\n\t<li>$0 \\leq A_i \\leq 10^9$ $(1 \\leq i \\leq N)$<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$N \\le 100$<\/p>\r\n","subtask2":"<p>$N \\le 3000$<\/p>\r\n","subtask3":"<p>No additional constraints<\/p>\r\n","sample_explain_1":"<p>If you divide the array into two&nbsp;segments&nbsp;$[1, 2]$ and&nbsp;$[3, 3]$, the&nbsp;sum of the levels of the new problems is&nbsp;$8$.<\/p>\r\n\r\n<p>$(5 \\oplus 3) + (2) = 8$<\/p>\r\n","sample_explain_2":"<p>If you divide the array into three segments&nbsp;$[1, 1]$, $[2, 3]$ and&nbsp;$[4, 4]$, the&nbsp;sum of the levels of the new problems is&nbsp;$18$.<\/p>\r\n\r\n<p>$(6) + (2 \\oplus 4) + (6) = 18$<\/p>\r\n","sample_explain_3":"<p>If you divide the array into one segment&nbsp;$[1, 4]$, the&nbsp;sum of the levels of the new problems is&nbsp;$15$.<\/p>\r\n\r\n<p>$(1 \\oplus 2 \\oplus 4 \\oplus 8)= 15$<\/p>\r\n"}]