(追記) (追記ここまで)

31719번 - UDP 스택 다국어

시간 제한	메모리 제한	제출	정답	맞힌 사람	정답 비율
1 초	1024 MB	665	187	155	30.452%

문제

UDP 마을에는 세 개의 신비한 스택이 있다. 이를 차례로 U스택, D스택, P스택이라 하자. 이 스택들은 특별해서 스택의 바닥을 열고 닫을 수 있다. 바닥이 열려 있는 스택에 원소를 삽입하면 그 즉시 바닥 아래로 떨어지며, 바닥이 닫혀 있는 스택의 바닥을 열면 저장되어 있던 원소들이 모두 바닥 아래로 떨어진다. 이때, 스택의 바닥에 가까운 쪽의 원소들이 더 먼저 바닥으로 떨어진다. 초기에는 U스택의 바닥만이 열려 있으며, D스택과 P스택의 바닥은 닫혀 있다.

어느 날, UDP 마을에서 길이가 $N$인 순열 $A$가 발견되었다. 포닉스는 다음 두 연산만을 사용할 수 있다.

순열 $A$의 가장 앞 원소를 세 스택 중 하나에 삽입한 후 순열에서 삭제한다. 단, 이 연산은 순열 $A$가 비어있지 않을 때만 가능하다.
현재 바닥이 열려 있는 스택을 닫은 후 바닥이 닫혀 있는 스택 중 하나를 골라 연다.

포닉스는 순열 $A$와 세 스택이 모두 빌 때까지 연산을 반복한 후, 먼저 떨어진 것이 앞에 오도록 원소들을 나열할 것이다. 포닉스가 원소들을 오름차순으로 재배열할 수 있을지 판별하여라.

입력

첫째 줄에 테스트케이스의 개수 $T$가 주어진다. $(1 \le T \le 500\ 000)$

각 테스트케이스의 첫째 줄에 순열의 길이 $N$이 주어진다. $(1 \le N \le 200\ 000)$

각 테스트케이스의 둘째 줄에 순열 $A$의 원소 $A_1, A_2, \cdots, A_N$이 공백으로 구분되어 주어진다. $A_i$는 1ドル$ 이상 $N$ 이하의 서로 다른 정수이다.

모든 테스트케이스에 대해 $N$의 합이 500ドル\ 000$ 이하임이 보장된다.

출력

각 테스트케이스에 대해 포닉스가 원소들을 오름차순으로 재배열하는 것이 가능하면 YES, 아니면 NO를 한 줄에 하나씩 순서대로 출력하여라.

제한

예제 입력 1

예제 출력 1

YES
YES
NO

힌트

[{"problem_id":"31719","problem_lang":"0","title":"UDP \uc2a4\ud0dd","description":"<p>UDP \ub9c8\uc744\uc5d0\ub294 \uc138 \uac1c\uc758 \uc2e0\ube44\ud55c \uc2a4\ud0dd\uc774 \uc788\ub2e4. \uc774\ub97c \ucc28\ub840\ub85c U\uc2a4\ud0dd, D\uc2a4\ud0dd, P\uc2a4\ud0dd\uc774\ub77c \ud558\uc790. \uc774 \uc2a4\ud0dd\ub4e4\uc740 \ud2b9\ubcc4\ud574\uc11c \uc2a4\ud0dd\uc758 \ubc14\ub2e5\uc744 \uc5f4\uace0 \ub2eb\uc744 \uc218 \uc788\ub2e4. \ubc14\ub2e5\uc774 \uc5f4\ub824 \uc788\ub294 \uc2a4\ud0dd\uc5d0 \uc6d0\uc18c\ub97c \uc0bd\uc785\ud558\uba74 \uadf8 \uc989\uc2dc \ubc14\ub2e5 \uc544\ub798\ub85c \ub5a8\uc5b4\uc9c0\uba70, \ubc14\ub2e5\uc774 \ub2eb\ud600 \uc788\ub294 \uc2a4\ud0dd\uc758 \ubc14\ub2e5\uc744 \uc5f4\uba74 \uc800\uc7a5\ub418\uc5b4 \uc788\ub358 \uc6d0\uc18c\ub4e4\uc774 \ubaa8\ub450 \ubc14\ub2e5 \uc544\ub798\ub85c \ub5a8\uc5b4\uc9c4\ub2e4. \uc774\ub54c, \uc2a4\ud0dd\uc758 \ubc14\ub2e5\uc5d0 \uac00\uae4c\uc6b4 \ucabd\uc758 \uc6d0\uc18c\ub4e4\uc774 \ub354 \uba3c\uc800 \ubc14\ub2e5\uc73c\ub85c \ub5a8\uc5b4\uc9c4\ub2e4. \ucd08\uae30\uc5d0\ub294 U\uc2a4\ud0dd\uc758 \ubc14\ub2e5\ub9cc\uc774 \uc5f4\ub824 \uc788\uc73c\uba70, D\uc2a4\ud0dd\uacfc P\uc2a4\ud0dd\uc758 \ubc14\ub2e5\uc740 \ub2eb\ud600 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc5b4\ub290 \ub0a0, UDP \ub9c8\uc744\uc5d0\uc11c \uae38\uc774\uac00 $N$\uc778 \uc21c\uc5f4 $A$\uac00 \ubc1c\uacac\ub418\uc5c8\ub2e4. \ud3ec\ub2c9\uc2a4\ub294 \ub2e4\uc74c \ub450 \uc5f0\uc0b0\ub9cc\uc744 \uc0ac\uc6a9\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc21c\uc5f4 $A$\uc758 \uac00\uc7a5 \uc55e \uc6d0\uc18c\ub97c \uc138 \uc2a4\ud0dd \uc911 \ud558\ub098\uc5d0 \uc0bd\uc785\ud55c \ud6c4 \uc21c\uc5f4\uc5d0\uc11c \uc0ad\uc81c\ud55c\ub2e4. \ub2e8, \uc774 \uc5f0\uc0b0\uc740 \uc21c\uc5f4 $A$\uac00 \ube44\uc5b4\uc788\uc9c0 \uc54a\uc744 \ub54c\ub9cc \uac00\ub2a5\ud558\ub2e4.<\/li>\r\n\t<li>\ud604\uc7ac \ubc14\ub2e5\uc774 \uc5f4\ub824 \uc788\ub294 \uc2a4\ud0dd\uc744 \ub2eb\uc740 \ud6c4 \ubc14\ub2e5\uc774 \ub2eb\ud600 \uc788\ub294 \uc2a4\ud0dd \uc911 \ud558\ub098\ub97c \uace8\ub77c \uc5f0\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ud3ec\ub2c9\uc2a4\ub294 \uc21c\uc5f4 $A$\uc640 \uc138 \uc2a4\ud0dd\uc774 \ubaa8\ub450 \ube4c \ub54c\uae4c\uc9c0 \uc5f0\uc0b0\uc744 \ubc18\ubcf5\ud55c \ud6c4, \uba3c\uc800 \ub5a8\uc5b4\uc9c4 \uac83\uc774 \uc55e\uc5d0 \uc624\ub3c4\ub85d \uc6d0\uc18c\ub4e4\uc744 \ub098\uc5f4\ud560 \uac83\uc774\ub2e4. \ud3ec\ub2c9\uc2a4\uac00 \uc6d0\uc18c\ub4e4\uc744 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc7ac\ubc30\uc5f4\ud560 \uc218 \uc788\uc744\uc9c0 \ud310\ubcc4\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \uac1c\uc218 $T$\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le T \\le 500\\ 000)$<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0 \uc21c\uc5f4\uc758 \uae38\uc774 $N$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. $(1 \\le N \\le 200\\ 000)$<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc758 \ub458\uc9f8 \uc904\uc5d0 \uc21c\uc5f4 $A$\uc758 \uc6d0\uc18c $A_1, A_2, \\cdots, A_N$\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. $A_i$\ub294 $1$ \uc774\uc0c1 $N$ \uc774\ud558\uc758 \uc11c\ub85c \ub2e4\ub978 \uc815\uc218\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 $N$\uc758 \ud569\uc774 $500\\ 000$ \uc774\ud558\uc784\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8\ucf00\uc774\uc2a4\uc5d0 \ub300\ud574 \ud3ec\ub2c9\uc2a4\uac00 \uc6d0\uc18c\ub4e4\uc744 \uc624\ub984\ucc28\uc21c\uc73c\ub85c \uc7ac\ubc30\uc5f4\ud558\ub294 \uac83\uc774 \uac00\ub2a5\ud558\uba74 <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span>, \uc544\ub2c8\uba74 <span style=\"color:#e74c3c;\"><code>NO<\/code><\/span>\ub97c \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc21c\uc11c\ub300\ub85c \ucd9c\ub825\ud558\uc5ec\ub77c.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"31719","problem_lang":"1","title":"UDP Stack","description":"<p>In the UDP town, there are three mysterious stacks. Let&#39;s call them U-stack, D-stack, and P-stack respectively. The stacks are special&nbsp;because the bottom can be opened and closed. When an element is inserted into a stack whose bottom is open, it immediately falls through the bottom, and if the bottom of a closed stack is opened, all the elements stored in it fall through&nbsp;the bottom.&nbsp;In this process, the elements closer to the bottom of the stack fall first. Initially, only the bottom of the U-stack is open, and the bottoms of the D-stack and P-stack are closed.<\/p>\r\n\r\n<p>One day, in the UDP town, a permutation $A$ of length $N$ was discovered. Ponix can only use the following two operations:<\/p>\r\n\r\n<ul>\r\n\t<li>Insert the first element of permutation $A$ into one of the three stacks and then delete it from the permutation.&nbsp;However, this operation is only possible when permutation $A$ is not empty.<\/li>\r\n\t<li>Close the currently open stack&#39;s bottom, then open one of the closed stacks&#39;&nbsp;bottom.<\/li>\r\n<\/ul>\r\n\r\n<p>Ponix will arrange in a row&nbsp;the elements such that the first element to fall will be positioned at the front, after repeating operations until permutation $A$ and all three stacks are empty. Determine if Ponix can rearrange the elements in ascending order.<\/p>\r\n","input":"<p>Each test consists of multiple test cases. The first line contains a single integer $T$, the number of test cases. $(1 \\le T \\le 500\\ 000)$<\/p>\r\n\r\n<p>The first line of each test case contains a single integer $N$, the length of the permutation. $(1 \\le N \\le 200\\ 000)$<\/p>\r\n\r\n<p>The second line of each test case contains $N$ space-separated integers $A_1, A_2, \\cdots, A_N$. Each $A_i$ is a distinct integer&nbsp;from $1$ to $N$, inclusive.<\/p>\r\n\r\n<p>It is guaranteed that the sum of the values of $N$ for all test cases does not exceed $500\\ 000$.<\/p>\r\n","output":"<p>For each test case, print <span style=\"color:#e74c3c;\"><code>YES<\/code><\/span> if Ponix can rearrange the elements in&nbsp;ascending order, and <code><span style=\"color:#e74c3c;\">NO<\/span><\/code> otherwise.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]