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30238번 - 카드 게임 다국어

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문제

$n$개의 카드가 덱에 쌓여 있다. 위에서 $i$번째 카드에는 정수 $a_{i}$가 적혀 있다. 카드에 적혀 있는 정수는 변하지 않는다.

성호는 혼자 게임을 하려고 한다. 처음에 성호의 점수는 0ドル$이다. 매 턴마다 성호는 다음 중 하나의 행동을 할 수 있다:

  • 현재 남아 있는 카드 개수보다 크지 않은 양의 홀수 $i$를 선택한다. 위에서 $i$번째 카드를 덱에서 제거하고 해당 카드에 적혀 있는 수를 점수에 더한다.
  • 현재 남아 있는 카드 개수보다 크지 않은 양의 짝수 $i$를 선택한다. 위에서 $i$번째 카드를 덱에서 제거한다.
  • 게임을 종료한다. 게임 종료 전에 모든 카드를 덱에서 제거하지 않아도 된다.

성호의 최종 점수의 최댓값을 구하여라.

입력

각 입력은 여러 개의 테스트 케이스로 이루어져 있다. 첫 번째 줄에 테스트 케이스의 개수 $t$가 주어진다(1ドル \le t \le 10^{4}$). 다음 줄부터 각각의 테스트 케이스가 주어진다.

각각의 테스트 케이스의 첫 번째 줄에 정수 $n$이 주어진다 (1ドル \le n \le 2 \cdot 10^{5}$).

두 번째 줄에 $n$개의 정수 $a_1, a_2, \ldots, a_n$이 공백으로 구분되어 주어진다 ($-10^{9} \le a_i \le 10^{9}$).

모든 테스트 케이스에서 $n$의 총합은 2ドル \cdot 10^{5}$를 넘지 않는다.

출력

각각의 테스트 케이스마다 정답을 출력한다.

제한

예제 입력 1

4
4
-4 1 -3 5
4
1 -2 3 -4
3
-1 3 -5
1
-1

예제 출력 1

5
4
2
0

노트

첫 번째 테스트 케이스에서, 성호는 다음 방법으로 5ドル$점을 획득할 수 있다:

  1. 첫 번째 턴에서, $i=2$를 선택한다. 성호의 점수는 0ドル$점으로 유지되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[-4, -3, 5]$가 된다.
  2. 두 번째 턴에서, $i=3$을 선택한다. 성호의 점수는 5ドル$점이 되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[-4, -3]$이 된다.
  3. 세 번째 턴에서, 게임을 종료한다. 최종 점수는 5ドル$점이다.

두 번째 테스트 케이스에서, 성호는 다음 방법으로 4ドル$점을 획득할 수 있다:

  1. 첫 번째 턴에서, $i=3$을 선택한다. 성호의 점수는 3ドル$점이 되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[1, -2, -4]$가 된다.
  2. 두 번째 턴에서, $i=1$을 선택한다. 성호의 점수는 4ドル$점이 되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[-2, -4]$가 된다.
  3. 세 번째 턴에서, 게임을 종료한다. 최종 점수는 4ドル$점이다.

세 번째 테스트 케이스에서, 성호는 다음 방법으로 2ドル$점을 획득할 수 있다:

  1. 첫 번째 턴에서, $i=1$을 선택한다. 성호의 점수는 $-1$점이 되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[3, -5]$가 된다.
  2. 두 번째 턴에서, $i=1$을 선택한다. 성호의 점수는 2ドル$점이 되고, 덱에 남은 카드에 적힌 수는 위부터 차례로 $[-5]$가 된다.
[{"problem_id":"30238","problem_lang":"0","title":"\uce74\ub4dc \uac8c\uc784","description":"<p>$n$\uac1c\uc758 \uce74\ub4dc\uac00 \ub371\uc5d0 \uc313\uc5ec \uc788\ub2e4. \uc704\uc5d0\uc11c $i$\ubc88\uc9f8 \uce74\ub4dc\uc5d0\ub294 \uc815\uc218 $a_{i}$\uac00 \uc801\ud600 \uc788\ub2e4. \uce74\ub4dc\uc5d0 \uc801\ud600 \uc788\ub294 \uc815\uc218\ub294 \ubcc0\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc131\ud638\ub294 \ud63c\uc790 \uac8c\uc784\uc744 \ud558\ub824\uace0 \ud55c\ub2e4. \ucc98\uc74c\uc5d0 \uc131\ud638\uc758 \uc810\uc218\ub294 $0$\uc774\ub2e4. \ub9e4 \ud134\ub9c8\ub2e4 \uc131\ud638\ub294 \ub2e4\uc74c \uc911 <strong>\ud558\ub098<\/strong>\uc758 \ud589\ub3d9\uc744 \ud560 \uc218 \uc788\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>\ud604\uc7ac \ub0a8\uc544 \uc788\ub294 \uce74\ub4dc \uac1c\uc218\ubcf4\ub2e4 \ud06c\uc9c0 \uc54a\uc740 \uc591\uc758 <strong>\ud640\uc218<\/strong> $i$\ub97c \uc120\ud0dd\ud55c\ub2e4. \uc704\uc5d0\uc11c $i$\ubc88\uc9f8 \uce74\ub4dc\ub97c \ub371\uc5d0\uc11c \uc81c\uac70\ud558\uace0 <strong>\ud574\ub2f9 \uce74\ub4dc\uc5d0 \uc801\ud600 \uc788\ub294 \uc218\ub97c \uc810\uc218\uc5d0 \ub354\ud55c\ub2e4<\/strong>.<\/li>\r\n\t<li>\ud604\uc7ac \ub0a8\uc544 \uc788\ub294 \uce74\ub4dc \uac1c\uc218\ubcf4\ub2e4 \ud06c\uc9c0 \uc54a\uc740 \uc591\uc758 <strong>\uc9dd\uc218<\/strong> $i$\ub97c \uc120\ud0dd\ud55c\ub2e4. \uc704\uc5d0\uc11c $i$\ubc88\uc9f8 \uce74\ub4dc\ub97c \ub371\uc5d0\uc11c \uc81c\uac70\ud55c\ub2e4.<\/li>\r\n\t<li>\uac8c\uc784\uc744 \uc885\ub8cc\ud55c\ub2e4. \uac8c\uc784 \uc885\ub8cc \uc804\uc5d0 \ubaa8\ub4e0 \uce74\ub4dc\ub97c \ub371\uc5d0\uc11c \uc81c\uac70\ud558\uc9c0 \uc54a\uc544\ub3c4 \ub41c\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc131\ud638\uc758 \ucd5c\uc885 \uc810\uc218\uc758 \ucd5c\ub313\uac12\uc744 \uad6c\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uac01 \uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab \ubc88\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 $t$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4($1 \\le t \\le 10^{4}$). \ub2e4\uc74c \uc904\ubd80\ud130 \uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \ubc88\uc9f8 \uc904\uc5d0 \uc815\uc218 $n$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4 ($1 \\le n \\le 2 \\cdot 10^{5}$).<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 $n$\uac1c\uc758 \uc815\uc218 $a_1, a_2, \\ldots, a_n$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4 ($-10^{9} \\le a_i \\le 10^{9}$).<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c $n$\uc758 \ucd1d\ud569\uc740 $2 \\cdot 10^{5}$\ub97c \ub118\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uc815\ub2f5\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uccab \ubc88\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c, \uc131\ud638\ub294 \ub2e4\uc74c \ubc29\ubc95\uc73c\ub85c $5$\uc810\uc744 \ud68d\ub4dd\ud560 \uc218 \uc788\ub2e4:<\/p>\r\n\r\n<ol>\r\n\t<li>\uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=2$\ub97c \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $0$\uc810\uc73c\ub85c \uc720\uc9c0\ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[-4, -3, 5]$\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=3$\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $5$\uc810\uc774 \ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[-4, -3]$\uc774 \ub41c\ub2e4.<\/li>\r\n\t<li>\uc138 \ubc88\uc9f8 \ud134\uc5d0\uc11c, \uac8c\uc784\uc744 \uc885\ub8cc\ud55c\ub2e4. \ucd5c\uc885 \uc810\uc218\ub294 $5$\uc810\uc774\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c, \uc131\ud638\ub294 \ub2e4\uc74c \ubc29\ubc95\uc73c\ub85c $4$\uc810\uc744 \ud68d\ub4dd\ud560 \uc218 \uc788\ub2e4:<\/p>\r\n\r\n<ol>\r\n\t<li>\uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=3$\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $3$\uc810\uc774 \ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[1, -2, -4]$\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=1$\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $4$\uc810\uc774 \ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[-2, -4]$\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\uc138 \ubc88\uc9f8 \ud134\uc5d0\uc11c, \uac8c\uc784\uc744 \uc885\ub8cc\ud55c\ub2e4. \ucd5c\uc885 \uc810\uc218\ub294 $4$\uc810\uc774\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc138 \ubc88\uc9f8 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0\uc11c, \uc131\ud638\ub294 \ub2e4\uc74c \ubc29\ubc95\uc73c\ub85c $2$\uc810\uc744 \ud68d\ub4dd\ud560 \uc218 \uc788\ub2e4:<\/p>\r\n\r\n<ol>\r\n\t<li>\uccab \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=1$\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $-1$\uc810\uc774 \ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[3, -5]$\uac00 \ub41c\ub2e4.<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \ud134\uc5d0\uc11c, $i=1$\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc131\ud638\uc758 \uc810\uc218\ub294 $2$\uc810\uc774 \ub418\uace0, \ub371\uc5d0 \ub0a8\uc740 \uce74\ub4dc\uc5d0 \uc801\ud78c \uc218\ub294 \uc704\ubd80\ud130 \ucc28\ub840\ub85c $[-5]$\uac00 \ub41c\ub2e4.<\/li>\r\n<\/ol>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"30238","problem_lang":"1","title":"Card Game","description":"<p>There are $n$ cards stacked in a deck. Initially, $a_{i}$ is written on the $i$-th card from the top. The value written on a card does not change.<\/p>\r\n\r\n<p>You will play a game. Initially your score is $0$. In each turn, you can do <strong>one<\/strong>&nbsp;of the following operations:<\/p>\r\n\r\n<ul>\r\n\t<li>Choose an odd$^{\\dagger}$ positive integer $i$, which is not greater than the number of cards left in the deck. Remove the $i$-th card from the top of the deck <strong>and add the number written on the card to your score<\/strong>. The remaining cards will be reindexed starting from the top.<\/li>\r\n\t<li>Choose an even$^{\\ddagger}$ positive integer $i$, which is not greater than the number of cards left in the deck. Remove the $i$-th card from the top of the deck. The remaining cards will be reindexed starting from the top.<\/li>\r\n\t<li>End the game. You can end the game whenever you want, you <strong>do not<\/strong>&nbsp;have to remove all cards from the initial deck.<\/li>\r\n<\/ul>\r\n\r\n<p>What is the maximum score you can get when the game ends?<\/p>\r\n\r\n<p>$^{\\dagger}$ An integer $i$ is odd, if there exists an integer $k$ such that $i = 2k + 1$.<\/p>\r\n\r\n<p>$^{\\ddagger}$ An integer $i$ is even, if there exists an integer $k$ such that $i = 2k$.<\/p>\r\n","input":"<p>Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \\le t \\le 10^{4}$). The description of the test cases follows.<\/p>\r\n\r\n<p>The first line of each test case contains a single integer $n$ ($1 \\le n \\le 2 \\cdot 10^{5}$).<\/p>\r\n\r\n<p>The second line of each test case contains $n$ integers $a_1, a_2, \\ldots, a_n$ ($-10^{9} \\le a_i \\le 10^{9}$).<\/p>\r\n\r\n<p>It is guaranteed that the sum of $n$ over all test cases does not exceed $2 \\cdot 10^{5}$.<\/p>\r\n","output":"<p>For each test case, print a single integer --- the maximum score you can get when the game ends.<\/p>\r\n","hint":"<p>In the first test case, one can get the score of $5$ as follows:<\/p>\r\n\r\n<ol>\r\n\t<li>In the first turn, choose $i=2$. Your score remains $0$ and the numbers written on the cards from the top will become $[-4, -3, 5]$.<\/li>\r\n\t<li>In the second turn, choose $i=3$. Your score will become $5$ and the numbers written on the cards from the top will become $[-4, -3]$.<\/li>\r\n\t<li>In the third turn, end the game with the score of $5$.<\/li>\r\n<\/ol>\r\n\r\n<p>In the second test case, one can get the score of $4$ as follows:<\/p>\r\n\r\n<ol>\r\n\t<li>In the first turn, choose $i=3$. Your score will become $3$ and the numbers written on the cards from the top will become $[1, -2, -4]$.<\/li>\r\n\t<li>In the second turn, choose $i=1$. Your score will become $4$ and the numbers written on the cards from the top will become $[-2, -4]$.<\/li>\r\n\t<li>In the third turn, end the game with the score of $4$.<\/li>\r\n<\/ol>\r\n\r\n<p>In the third test case, one can get the score of $2$ as follows:<\/p>\r\n\r\n<ol>\r\n\t<li>In the first turn, choose $i=1$. Your score will become $-1$ and the numbers written on the cards from the top will become $[3, -5]$.<\/li>\r\n\t<li>In the second turn, choose $i=1$. Your score will become $2$ and the numbers written on the cards from the top will become $[-5]$.<\/li>\r\n\t<li>In the third turn, end the game with the score of $2$.<\/li>\r\n<\/ol>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English"}]

출처

Contest > Codeforces > Codeforces Round 899 (Div. 2) C번

(追記) (追記ここまで)

출처

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