시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 478 92 56 18.983%

문제

고창영은 스택을 조금 변형해서 고스택을 만들었다.

고스택은 숫자만을 저장할 수 있고, 다음과 같은 10가지 연산을 수행할 수 있다.

편의상 스택의 가장 위에 저장된 수를 첫번째 수라고 하고, 그 다음은 차례대로 두번째 수, 세번째 수라고 한다.

  • NUM X: X를 스택의 가장 위에 저장한다. (0 ≤ X ≤ 109)
  • POP: 스택 가장 위의 숫자를 제거한다.
  • INV: 첫번째 수의 부호를 바꾼다. (42 -> -42)
  • DUP: 첫번째 숫자를 하나 더 스택의 가장 위에 저장한다.
  • SWP: 첫번째 숫자와 두번째 숫자의 위치를 서로 바꾼다.
  • ADD: 첫번째 숫자와 두번째 숫자를 더한다.
  • SUB: 첫번째 숫자와 두번째 숫자를 뺀다. (두번째 - 첫번째)
  • MUL: 첫번째 숫자와 두번째 숫자를 곱한다.
  • DIV: 첫번째 숫자로 두번째 숫자를 나눈 몫을 저장한다. 두번째 숫자가 피제수, 첫번째 숫자가 제수이다.
  • MOD: 첫번째 숫자로 두번째 숫자를 나눈 나머지를 저장한다. 두번째 숫자가 피제수, 첫번째 숫자가 제수이다.

이항 연산자의 경우에 첫번째 숫자가 오른쪽에 있는 수이고, 두번째 숫자가 왼쪽에 있는 수이다. 또, 연산을 수행하기 전에 두 숫자를 모두 스택에서 제거한 뒤, 결과를 다시 스택에 저장하는 것이다.

숫자가 부족해서 연산을 수행할 수 없을 때, 0으로 나눴을 때 (DIV, MOD), 연산 결과의 절대값이 109를 넘어갈 때는 모두 프로그램 에러이다.

음수 나눗셈에 대한 모호함을 피하기 위해 다음과 같이 계산한다. 나눗셈의 피연산자에 음수가 있을 때는, 그 수를 절대값을 씌운 뒤 계산한다. 그리고 나서 몫과 나머지의 부호는 다음과 같이 결정한다. 피연산자중 음수가 한 개일때는 몫의 부호가 음수이다. 이 경우를 제외하면 몫의 부호는 항상 양수이다. 나머지의 부호는 피제수의 부호와 같다. 따라서, 13 div -4 = -3, -13 mod 4 = -1, -13 mod -4 = -1이다.

프로그램 에러가 발생했을 경우에는, 현재 프로그램의 수행을 멈추고, 그 다음 어떤 명령도 수행하지 않는다.

입력

입력은 기계 여러 대의 설명으로 이루어져 있다. 각 기계의 설명은 프로그램과 입력영역으로 나누어져 있다.

프로그램은 명령어로 이루어져 있고, 명령어는 한 줄에 하나씩 있다. 각 명령은 문제 설명에 나와있는 대문자 알파벳 3글자이고, 다른 글자는 주어지지 않는다. NUM의 경우에는 명령어 다음에 숫자가 주어지며, 이 숫자는 0보다 크거나 같고, 109보다 작거나 같은 정수이다. NUM과 숫자는 공백으로 구분되어져 있다. 각 프로그램은 END가 나오면 끝난다.

입력영역은 첫째 줄에 프로그램 수행 횟수 N이 있다. (0 ≤ N ≤ 10,000) 다음 N개의 줄에는 한 줄에 하나씩 입력값 Vi가 있다. (0 ≤ Vi ≤ 109) 각 입력값에 대해서 프로그램을 한 번씩 수행해야 하고, 이 수행은 모두 독립적이다. 매번 프로그램을 수행할 때, 스택에 들어있는 값은 입력값 Vi 하나이다.

각각의 기계 설명은 빈 줄로 구분되어져 있다. QUIT이 나오면 다음 기계 설명이 없다는 뜻이다. 명령어가 100,000개를 넘어가는 경우와 스택이 수행될 때, 1,000개 이상의 숫자를 저장하는 경우는 없다.

출력

각각의 입력값에 대해서, 해당하는 프로그램을 수행한 뒤, 출력값을 출력하면 된다. 출력값이란 스택에 저장되어 있는 숫자이다.

만약, 프로그램 에러가 발생하거나, 모든 수행이 종료됐을 때 스택에 저장되어 있는 숫자가 1개가 아니라면, "ERROR"를 출력한다.

각 기계에 대한 출력값을 모두 출력한 뒤에는 빈 줄을 하나 출력해야 한다.

예제 입력 1

DUP
MUL
NUM 2
ADD
END
3
1
10
50

NUM 1
NUM 1
ADD
END
2
42
43

NUM 600000000
ADD
END
3
0
600000000
1

QUIT

예제 출력 1

3
102
2502

ERROR
ERROR

600000000
ERROR
600000001
[{"problem_id":"3425","problem_lang":"0","title":"\uace0\uc2a4\ud0dd","description":"<p>\uace0\ucc3d\uc601\uc740 \uc2a4\ud0dd\uc744 \uc870\uae08 \ubcc0\ud615\ud574\uc11c \uace0\uc2a4\ud0dd\uc744 \ub9cc\ub4e4\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uace0\uc2a4\ud0dd\uc740 \uc22b\uc790\ub9cc\uc744 \uc800\uc7a5\ud560 \uc218 \uc788\uace0, \ub2e4\uc74c\uacfc \uac19\uc740 10\uac00\uc9c0 \uc5f0\uc0b0\uc744 \uc218\ud589\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud3b8\uc758\uc0c1 \uc2a4\ud0dd\uc758 \uac00\uc7a5 \uc704\uc5d0 \uc800\uc7a5\ub41c \uc218\ub97c \uccab\ubc88\uc9f8 \uc218\ub77c\uace0 \ud558\uace0, \uadf8 \ub2e4\uc74c\uc740 \ucc28\ub840\ub300\ub85c \ub450\ubc88\uc9f8 \uc218, \uc138\ubc88\uc9f8 \uc218\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li><strong>NUM X<\/strong>: X\ub97c \uc2a4\ud0dd\uc758 \uac00\uc7a5 \uc704\uc5d0 \uc800\uc7a5\ud55c\ub2e4. (0 &le; X &le; 10<sup>9<\/sup>)<\/li>\r\n\t<li><strong>POP<\/strong>: \uc2a4\ud0dd \uac00\uc7a5 \uc704\uc758 \uc22b\uc790\ub97c \uc81c\uac70\ud55c\ub2e4.<\/li>\r\n\t<li><strong>INV<\/strong>: \uccab\ubc88\uc9f8 \uc218\uc758 \ubd80\ud638\ub97c \ubc14\uafbc\ub2e4. (42 -&gt; -42)<\/li>\r\n\t<li><strong>DUP<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\ub97c \ud558\ub098 \ub354 \uc2a4\ud0dd\uc758 \uac00\uc7a5 \uc704\uc5d0 \uc800\uc7a5\ud55c\ub2e4.<\/li>\r\n\t<li><strong>SWP<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\uc640 \ub450\ubc88\uc9f8 \uc22b\uc790\uc758 \uc704\uce58\ub97c \uc11c\ub85c \ubc14\uafbc\ub2e4.<\/li>\r\n\t<li><strong>ADD<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\uc640 \ub450\ubc88\uc9f8 \uc22b\uc790\ub97c \ub354\ud55c\ub2e4.<\/li>\r\n\t<li><strong>SUB<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\uc640 \ub450\ubc88\uc9f8 \uc22b\uc790\ub97c \ube80\ub2e4. (\ub450\ubc88\uc9f8 - \uccab\ubc88\uc9f8)<\/li>\r\n\t<li><strong>MUL<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\uc640 \ub450\ubc88\uc9f8 \uc22b\uc790\ub97c \uacf1\ud55c\ub2e4.<\/li>\r\n\t<li><strong>DIV<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\ub85c \ub450\ubc88\uc9f8 \uc22b\uc790\ub97c \ub098\ub208 \ubaab\uc744 \uc800\uc7a5\ud55c\ub2e4. \ub450\ubc88\uc9f8 \uc22b\uc790\uac00 \ud53c\uc81c\uc218, \uccab\ubc88\uc9f8 \uc22b\uc790\uac00 \uc81c\uc218\uc774\ub2e4.<\/li>\r\n\t<li><strong>MOD<\/strong>: \uccab\ubc88\uc9f8 \uc22b\uc790\ub85c \ub450\ubc88\uc9f8 \uc22b\uc790\ub97c \ub098\ub208 \ub098\uba38\uc9c0\ub97c \uc800\uc7a5\ud55c\ub2e4. \ub450\ubc88\uc9f8 \uc22b\uc790\uac00 \ud53c\uc81c\uc218, \uccab\ubc88\uc9f8 \uc22b\uc790\uac00 \uc81c\uc218\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/stmc.png\" style=\"height:100px; width:514px\" \/><\/p>\r\n\r\n<p>\uc774\ud56d \uc5f0\uc0b0\uc790\uc758 \uacbd\uc6b0\uc5d0 \uccab\ubc88\uc9f8 \uc22b\uc790\uac00 \uc624\ub978\ucabd\uc5d0 \uc788\ub294 \uc218\uc774\uace0, \ub450\ubc88\uc9f8 \uc22b\uc790\uac00 \uc67c\ucabd\uc5d0 \uc788\ub294 \uc218\uc774\ub2e4. \ub610, \uc5f0\uc0b0\uc744 \uc218\ud589\ud558\uae30 \uc804\uc5d0 \ub450 \uc22b\uc790\ub97c \ubaa8\ub450 \uc2a4\ud0dd\uc5d0\uc11c \uc81c\uac70\ud55c \ub4a4, \uacb0\uacfc\ub97c \ub2e4\uc2dc \uc2a4\ud0dd\uc5d0 \uc800\uc7a5\ud558\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc22b\uc790\uac00 \ubd80\uc871\ud574\uc11c \uc5f0\uc0b0\uc744 \uc218\ud589\ud560 \uc218 \uc5c6\uc744 \ub54c, 0\uc73c\ub85c \ub098\ub234\uc744 \ub54c (DIV, MOD), \uc5f0\uc0b0 \uacb0\uacfc\uc758 \uc808\ub300\uac12\uc774 10<sup>9<\/sup>\ub97c \ub118\uc5b4\uac08 \ub54c\ub294 \ubaa8\ub450 \ud504\ub85c\uadf8\ub7a8 \uc5d0\ub7ec\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc74c\uc218 \ub098\ub217\uc148\uc5d0 \ub300\ud55c \ubaa8\ud638\ud568\uc744 \ud53c\ud558\uae30 \uc704\ud574 \ub2e4\uc74c\uacfc \uac19\uc774 \uacc4\uc0b0\ud55c\ub2e4. \ub098\ub217\uc148\uc758 \ud53c\uc5f0\uc0b0\uc790\uc5d0 \uc74c\uc218\uac00 \uc788\uc744 \ub54c\ub294, \uadf8 \uc218\ub97c \uc808\ub300\uac12\uc744 \uc50c\uc6b4 \ub4a4 \uacc4\uc0b0\ud55c\ub2e4. \uadf8\ub9ac\uace0 \ub098\uc11c \ubaab\uacfc \ub098\uba38\uc9c0\uc758 \ubd80\ud638\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uacb0\uc815\ud55c\ub2e4. \ud53c\uc5f0\uc0b0\uc790\uc911 \uc74c\uc218\uac00 \ud55c \uac1c\uc77c\ub54c\ub294 \ubaab\uc758 \ubd80\ud638\uac00 \uc74c\uc218\uc774\ub2e4. \uc774 \uacbd\uc6b0\ub97c \uc81c\uc678\ud558\uba74 \ubaab\uc758 \ubd80\ud638\ub294 \ud56d\uc0c1 \uc591\uc218\uc774\ub2e4. \ub098\uba38\uc9c0\uc758 \ubd80\ud638\ub294 \ud53c\uc81c\uc218\uc758 \ubd80\ud638\uc640 \uac19\ub2e4. \ub530\ub77c\uc11c, 13 div -4 = -3, -13 mod 4 = -1, -13 mod -4 = -1\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud504\ub85c\uadf8\ub7a8 \uc5d0\ub7ec\uac00 \ubc1c\uc0dd\ud588\uc744 \uacbd\uc6b0\uc5d0\ub294, \ud604\uc7ac \ud504\ub85c\uadf8\ub7a8\uc758 \uc218\ud589\uc744 \uba48\ucd94\uace0, \uadf8 \ub2e4\uc74c \uc5b4\ub5a4 \uba85\ub839\ub3c4 \uc218\ud589\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uae30\uacc4 \uc5ec\ub7ec \ub300\uc758 \uc124\uba85\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \uae30\uacc4\uc758 \uc124\uba85\uc740 \ud504\ub85c\uadf8\ub7a8\uacfc \uc785\ub825\uc601\uc5ed\uc73c\ub85c \ub098\ub204\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ud504\ub85c\uadf8\ub7a8\uc740 \uba85\ub839\uc5b4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uba85\ub839\uc5b4\ub294 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc788\ub2e4. \uac01 \uba85\ub839\uc740 \ubb38\uc81c \uc124\uba85\uc5d0 \ub098\uc640\uc788\ub294 \ub300\ubb38\uc790 \uc54c\ud30c\ubcb3 3\uae00\uc790\uc774\uace0, \ub2e4\ub978 \uae00\uc790\ub294 \uc8fc\uc5b4\uc9c0\uc9c0 \uc54a\ub294\ub2e4. NUM\uc758 \uacbd\uc6b0\uc5d0\ub294 \uba85\ub839\uc5b4 \ub2e4\uc74c\uc5d0 \uc22b\uc790\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc774 \uc22b\uc790\ub294 0\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, 10<sup>9<\/sup>\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc815\uc218\uc774\ub2e4. NUM\uacfc \uc22b\uc790\ub294 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud504\ub85c\uadf8\ub7a8\uc740 END\uac00 \ub098\uc624\uba74 \ub05d\ub09c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc601\uc5ed\uc740 \uccab\uc9f8 \uc904\uc5d0 \ud504\ub85c\uadf8\ub7a8 \uc218\ud589 \ud69f\uc218 N\uc774 \uc788\ub2e4. (0 &le; N &le; 10,000) \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc785\ub825\uac12 V<sub>i<\/sub>\uac00 \uc788\ub2e4. (0 &le; V<sub>i<\/sub> &le; 10<sup>9<\/sup>) \uac01 \uc785\ub825\uac12\uc5d0 \ub300\ud574\uc11c \ud504\ub85c\uadf8\ub7a8\uc744 \ud55c \ubc88\uc529 \uc218\ud589\ud574\uc57c \ud558\uace0, \uc774 \uc218\ud589\uc740 \ubaa8\ub450 \ub3c5\ub9bd\uc801\uc774\ub2e4. \ub9e4\ubc88 \ud504\ub85c\uadf8\ub7a8\uc744 \uc218\ud589\ud560 \ub54c, \uc2a4\ud0dd\uc5d0 \ub4e4\uc5b4\uc788\ub294 \uac12\uc740 \uc785\ub825\uac12 V<sub>i<\/sub> \ud558\ub098\uc774\ub2e4.<\/p>\r\n\r\n<p>\uac01\uac01\uc758 \uae30\uacc4 \uc124\uba85\uc740 \ube48 \uc904\ub85c \uad6c\ubd84\ub418\uc5b4\uc838 \uc788\ub2e4. QUIT\uc774 \ub098\uc624\uba74 \ub2e4\uc74c \uae30\uacc4 \uc124\uba85\uc774 \uc5c6\ub2e4\ub294 \ub73b\uc774\ub2e4. \uba85\ub839\uc5b4\uac00 100,000\uac1c\ub97c \ub118\uc5b4\uac00\ub294 \uacbd\uc6b0\uc640 \uc2a4\ud0dd\uc774 \uc218\ud589\ub420 \ub54c, 1,000\uac1c \uc774\uc0c1\uc758 \uc22b\uc790\ub97c \uc800\uc7a5\ud558\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\uac01\uac01\uc758 \uc785\ub825\uac12\uc5d0 \ub300\ud574\uc11c, \ud574\ub2f9\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc218\ud589\ud55c \ub4a4, \ucd9c\ub825\uac12\uc744 \ucd9c\ub825\ud558\uba74 \ub41c\ub2e4. \ucd9c\ub825\uac12\uc774\ub780 \uc2a4\ud0dd\uc5d0 \uc800\uc7a5\ub418\uc5b4 \uc788\ub294 \uc22b\uc790\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc57d, \ud504\ub85c\uadf8\ub7a8 \uc5d0\ub7ec\uac00 \ubc1c\uc0dd\ud558\uac70\ub098, \ubaa8\ub4e0 \uc218\ud589\uc774 \uc885\ub8cc\ub410\uc744 \ub54c \uc2a4\ud0dd\uc5d0 \uc800\uc7a5\ub418\uc5b4 \uc788\ub294 \uc22b\uc790\uac00 1\uac1c\uac00 \uc544\ub2c8\ub77c\uba74, &quot;ERROR&quot;\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01 \uae30\uacc4\uc5d0 \ub300\ud55c \ucd9c\ub825\uac12\uc744 \ubaa8\ub450 \ucd9c\ub825\ud55c \ub4a4\uc5d0\ub294 \ube48 \uc904\uc744 \ud558\ub098 \ucd9c\ub825\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3425","problem_lang":"1","title":"Stack Machine Executor","description":"<p>Many ciphers can be computed much faster using various machines and automata. In this problem, we will focus on one particular type of machines called stack machine. Its name comes from the fact that the machine operates with the well-known data structure &mdash; stack. The later-stored values are on the top, older values at the bottom. Machine instructions typically manipulate the top of the stack only.<\/p>\r\n\r\n<p>Our stack machine is relatively simple: It works with integer numbers only, it has no storage beside the stack (no registers etc.) and no special input or output devices. The set of instructions is as follows:<\/p>\r\n\r\n<ul>\r\n\t<li><strong>NUM X<\/strong>, where X is a non-negative integer number, 0 &le; X &le; 10<sup>9<\/sup>. The NUM instruction stores the number X on top of the stack. It is the only parametrized instruction.<\/li>\r\n\t<li><strong>POP<\/strong>: removes the top number from the stack.<\/li>\r\n\t<li><strong>INV<\/strong>: changes the sign of the top-most number. (42 &rarr; &minus;42)<\/li>\r\n\t<li><strong>DUP<\/strong>: duplicates the top-most number on the stack.<\/li>\r\n\t<li><strong>SWP<\/strong>: swaps (exchanges) the position of two top-most numbers.<\/li>\r\n\t<li><strong>ADD<\/strong>: adds two numbers on the top of the stack.<\/li>\r\n\t<li><strong>SUB<\/strong>: subtracts the top-most number from the &ldquo;second one&rdquo; (the one below).<\/li>\r\n\t<li><strong>MUL<\/strong>: multiplies two numbers on the top of the stack.<\/li>\r\n\t<li><strong>DIV<\/strong>: integer divison of two numbers on the top. The top-most number becomes divisor, the one below dividend. The quotient will be stored as the result.<\/li>\r\n\t<li><strong>MOD<\/strong>: modulo operation. The operands are the same as for the division but the remainder is stored as the result.<\/li>\r\n<\/ul>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/stmc.png\" style=\"height:100px; opacity:0.9; width:514px\" \/><\/p>\r\n\r\n<p>All binary operations consider the top-most number to be the &ldquo;right&rdquo; operand, the second number the &ldquo;left&rdquo; one. All of them remove both operands from the stack and place the result on top in place of the original numbers.<\/p>\r\n\r\n<p>If there are not enough numbers on the stack for an instruction (one or two), the execution of such an instruction will result into a program failure. A failure also occurs if a divisor becomes zero (for DIV or MOD) or if the result of any operation should be more than 10<sup>9<\/sup> in absolute value. This means that the machine only operates with numbers between &minus;1 000 000 000 and 1 000 000 000, inclusive.<\/p>\r\n\r\n<p>To avoid ambiguities while working with negative divisors and remainders: If some operand of a division operation is negative, the absolute value of the result should always be computed with absolute values of operands, and the sign is determined as follows: The quotient is negative if (and only if) exactly one of the operands is negative. The remainder has the same sign as the dividend. Thus, 13 div &minus;4 = &minus;3, &minus;13 mod 4 = &minus;1, &minus;13 mod &minus;4 = &minus;1, etc<\/p>\r\n\r\n<p>If a failure occurs for any reason, the machine stops the execution of the current program and no other instructions are evaluated in that program run.<\/p>\r\n","input":"<p>The input contains description of several machines. Each machine is described by two parts: the program and the input section.<\/p>\r\n\r\n<p>The program is given by a series of instructions, one per line. Every instruction is given by three uppercase letters and there must not be any other characters. The only exception is the NUM instruction, which has exactly one space after the three letters followed by a non-negative integer number between 0 and 10<sup>9<\/sup>. The only allowed instructions are those de\ufb01ned above. Each program is terminated by a line containing the word &ldquo;END&rdquo; (and nothing else).<\/p>\r\n\r\n<p>The input section starts with an integer N (0 &le; N &le; 10 000), the number of program executions. The next N lines contain one number each, specifying an input value V<sub>i<\/sub>, 0 &le; V<sub>i<\/sub> &le; 10<sup>9<\/sup>. The program should be executed once for each of these values independently, every execution starting with the stack containing one number &mdash; the input value V<sub>i<\/sub>.<\/p>\r\n\r\n<p>There is one empty line at the and of each machine description. The last machine is followed by a line containing the word &ldquo;QUIT&rdquo;. No program will contain more than 100 000 instructions and no program requires more than 1 000 numbers on the stack in any moment during its execution.<\/p>\r\n","output":"<p>For each input value, print one line containing the output value for the corresponding execution, i.e., the one number that will be on the stack after the program executes with the initial stack containing only the input number.<\/p>\r\n\r\n<p>If there is a program failure during the execution or if the stack size is incorrect at the end of the run (either empty or there are more numbers than one), print the word &ldquo;ERROR&rdquo; instead.<\/p>\r\n\r\n<p>Print one empty line after each machine, including the last one.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Europe > Central European Regional Contest > CERC 2011 J번

  • 문제를 번역한 사람: baekjoon
  • 문제의 오타를 찾은 사람: jh05013
  • 데이터를 추가한 사람: kdk8361