시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

\(\odot : \left\{0, 1, \dots , 9 \right\} \times \left\{0, 1, \dots , 9 \right\} \rightarrow \left\{0, 1, \dots , 9 \right\} \) 인 연산자 \(\odot\)가 있다. 이 연산자는 \(0 \odot 0 = 0\) 을 만족한다고 한다.

또다른 연산자 \(\otimes : \mathbb{Z}_{0+} \times \mathbb{Z}_{0+} \rightarrow \mathbb{Z}_{0+}\) 는 연산자 \(\odot\) 을 이용해서 정의가 가능한데, \(a \otimes b\) 는 각 자리수마다 (\(a\)의 i번째 자리 수) \(\odot\) (\(b\)의 i번째 자리 수) 의 결과값을 i번째 자리 수로 사용한 숫자가 결과값이 된다.

예를 들어 \(a \odot b (a \times b) % 10\) 으로 정의되었다면 \(5566 \otimes 239\) 의 결과값을 구하는 과정은 아래와 같다.

\( \begin{align*} 5566& \\ \underline{\otimes \quad 239}& \\ ????& \end{align*} \) →  \( \begin{align*} 5566& \\ \underline{\otimes \quad 0239}& \\ ????& \end{align*} \) → \(  \begin{align*} 5& \\ \underline{\odot \quad 0}& \\ 0& \end{align*} \) \( \begin{align*} 5& \\ \underline{\odot \quad 2}& \\ 0& \end{align*} \) \( \begin{align*} 6& \\ \underline{\odot \quad 3}& \\ 8& \end{align*} \) \(\begin{align*} 6& \\ \underline{\odot \quad 9}& \\ 4& \end{align*} \) → \(  \begin{align*} 5566& \\ \underline{\otimes \quad 0239}& \\ 0084& \end{align*} \) → \(  \begin{align*} 5566& \\ \underline{\otimes \quad 239}& \\ 84& \end{align*}  \)

연산자 \(\odot\)의 내용과 두 음이아닌 정수 \(a\), \(b\)가 주어졌을 때 (\(a \le b\)), \(a \otimes (a + 1) \otimes (a + 2) \otimes \dots \otimes (b - 1) \otimes b\) 를 구하여라.

\(\otimes\)연산자의 계산 순서는 왼쪽부터 계산한다. 즉, \(a \otimes b \otimes c\) = \((a \otimes b) \otimes c\)로 취급한다.

입력

첫 10줄 각각에는 10개의 수가 주어진다. \(i\)번째 줄의 \(j\)번재 숫자는 \((i−1) \odot (j−1)\) 의 결과값을 나타낸다. \(0 \odot 0\) 은 항상 \(0\)이다.

이어 11번째 줄에는 2개의 정수 \(a\) \(b\)가 주어진다. (0 ≤ \(a\) ≤ \(b\) ≤ 1018)

출력

\(a\)부터 \(b\)까지 모든 수를 \(\otimes\) 연산한 결과값을 출력한다. 불필요한 0은 출력하지 않는다.

예제 입력 1

0 1 2 3 4 5 6 7 8 9
1 2 3 4 5 6 7 8 9 0
2 3 4 5 6 7 8 9 0 1
3 4 5 6 7 8 9 0 1 2
4 5 6 7 8 9 0 1 2 3
5 6 7 8 9 0 1 2 3 4
6 7 8 9 0 1 2 3 4 5
7 8 9 0 1 2 3 4 5 6
8 9 0 1 2 3 4 5 6 7
9 0 1 2 3 4 5 6 7 8
0 10

예제 출력 1

15
[{"problem_id":"3519","problem_lang":"0","title":"\uacc4\uc0b0\uc655 \uc5f0\uc0b0\uad70","description":"<p>\\(\\odot : \\left\\{0, 1, \\dots , 9 \\right\\} \\times \\left\\{0, 1, \\dots , 9 \\right\\} \\rightarrow \\left\\{0, 1, \\dots , 9 \\right\\} \\) \uc778 \uc5f0\uc0b0\uc790 \\(\\odot\\)\uac00 \uc788\ub2e4. \uc774 \uc5f0\uc0b0\uc790\ub294 \\(0 \\odot 0 = 0\\)&nbsp;\uc744 \ub9cc\uc871\ud55c\ub2e4\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub610\ub2e4\ub978 \uc5f0\uc0b0\uc790 \\(\\otimes : \\mathbb{Z}_{0+} \\times \\mathbb{Z}_{0+} \\rightarrow \\mathbb{Z}_{0+}\\)&nbsp;\ub294 \uc5f0\uc0b0\uc790 \\(\\odot\\) \uc744 \uc774\uc6a9\ud574\uc11c \uc815\uc758\uac00 \uac00\ub2a5\ud55c\ub370, \\(a \\otimes b\\) \ub294 \uac01 \uc790\ub9ac\uc218\ub9c8\ub2e4 (\\(a\\)\uc758 i\ubc88\uc9f8 \uc790\ub9ac \uc218) \\(\\odot\\)&nbsp;(\\(b\\)\uc758 i\ubc88\uc9f8 \uc790\ub9ac \uc218) \uc758 \uacb0\uacfc\uac12\uc744 i\ubc88\uc9f8 \uc790\ub9ac \uc218\ub85c \uc0ac\uc6a9\ud55c \uc22b\uc790\uac00 \uacb0\uacfc\uac12\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4 \\(a \\odot b (a \\times b) % 10\\) \uc73c\ub85c \uc815\uc758\ub418\uc5c8\ub2e4\uba74 \\(5566 \\otimes&nbsp;239\\) \uc758 \uacb0\uacfc\uac12\uc744 \uad6c\ud558\ub294 \uacfc\uc815\uc740 \uc544\ub798\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<p style=\"text-align:center\">\\( \\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 239}&amp; \\\\ ????&amp; \\end{align*} \\) &rarr; &nbsp;\\( \\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 0239}&amp; \\\\ ????&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5&amp; \\\\ \\underline{\\odot \\quad 0}&amp; \\\\ 0&amp; \\end{align*} \\) \\( \\begin{align*} 5&amp; \\\\ \\underline{\\odot \\quad 2}&amp; \\\\ 0&amp; \\end{align*} \\) \\( \\begin{align*} 6&amp; \\\\ \\underline{\\odot \\quad 3}&amp; \\\\ 8&amp; \\end{align*} \\) \\(\\begin{align*} 6&amp; \\\\ \\underline{\\odot \\quad 9}&amp; \\\\ 4&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 0239}&amp; \\\\ 0084&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 239}&amp; \\\\ 84&amp; \\end{align*} &nbsp;\\)<\/p>\r\n\r\n<p>\uc5f0\uc0b0\uc790 \\(\\odot\\)\uc758 \ub0b4\uc6a9\uacfc \ub450 \uc74c\uc774\uc544\ub2cc \uc815\uc218 \\(a\\), \\(b\\)\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c (\\(a \\le b\\)),&nbsp;\\(a \\otimes (a + 1) \\otimes (a + 2) \\otimes \\dots \\otimes (b - 1) \\otimes b\\) \ub97c \uad6c\ud558\uc5ec\ub77c.<\/p>\r\n\r\n<p>\\(\\otimes\\)\uc5f0\uc0b0\uc790\uc758 \uacc4\uc0b0 \uc21c\uc11c\ub294 \uc67c\ucabd\ubd80\ud130 \uacc4\uc0b0\ud55c\ub2e4. \uc989, \\(a \\otimes b \\otimes c\\)&nbsp;= \\((a \\otimes b) \\otimes c\\)\ub85c \ucde8\uae09\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab 10\uc904 \uac01\uac01\uc5d0\ub294 10\uac1c\uc758 \uc218\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \\(i\\)\ubc88\uc9f8 \uc904\uc758 \\(j\\)\ubc88\uc7ac \uc22b\uc790\ub294 \\((i&minus;1) \\odot (j&minus;1)\\) \uc758 \uacb0\uacfc\uac12\uc744 \ub098\ud0c0\ub0b8\ub2e4. \\(0 \\odot 0\\) \uc740 \ud56d\uc0c1 \\(0\\)\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc774\uc5b4 11\ubc88\uc9f8 \uc904\uc5d0\ub294 2\uac1c\uc758 \uc815\uc218 \\(a\\) \\(b\\)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; \\(a\\) &le; \\(b\\) &le; 10<sup>18<\/sup>)<\/p>\r\n","output":"<p>\\(a\\)\ubd80\ud130 \\(b\\)\uae4c\uc9c0 \ubaa8\ub4e0 \uc218\ub97c \\(\\otimes\\) \uc5f0\uc0b0\ud55c \uacb0\uacfc\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4. \ubd88\ud544\uc694\ud55c 0\uc740 \ucd9c\ub825\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3519","problem_lang":"1","title":"Binary Operation","description":"<p>Consider a binary operation \\(\\odot\\) defined on digits 0 to 9, \\(\\odot : \\left\\{0, 1, \\dots , 9 \\right\\} \\times \\left\\{0, 1, \\dots , 9 \\right\\} \\rightarrow \\left\\{0, 1, \\dots , 9 \\right\\} \\), such that \\(0 \\odot 0 = 0\\).<\/p>\r\n\r\n<p>A binary operation \\(\\otimes\\) is a generalization of \\(\\odot\\) to the set of non-negative integers, \\(\\otimes : \\mathbb{Z}_{0+} \\times \\mathbb{Z}_{0+} \\rightarrow \\mathbb{Z}_{0+}\\). The result of \\(a \\otimes b\\) is defined in the following way: if one of the numbers \\(a\\) and \\(b\\) has fewer digits than the other in decimal notation, then append leading zeroes to it, so that the numbers are of the same length; then apply the operation \\(\\odot\\) digit-wise to the corresponding digits of \\(a\\) and \\(b\\).<\/p>\r\n\r\n<p style=\"text-align: center;\">\\( \\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 239}&amp; \\\\ ????&amp; \\end{align*} \\) &rarr; &nbsp;\\( \\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 0239}&amp; \\\\ ????&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5&amp; \\\\ \\underline{\\odot \\quad 0}&amp; \\\\ 0&amp; \\end{align*} \\) \\( \\begin{align*} 5&amp; \\\\ \\underline{\\odot \\quad 2}&amp; \\\\ 0&amp; \\end{align*} \\) \\( \\begin{align*} 6&amp; \\\\ \\underline{\\odot \\quad 3}&amp; \\\\ 8&amp; \\end{align*} \\) \\(\\begin{align*} 6&amp; \\\\ \\underline{\\odot \\quad 9}&amp; \\\\ 4&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 0239}&amp; \\\\ 0084&amp; \\end{align*} \\) &rarr; \\( &nbsp;\\begin{align*} 5566&amp; \\\\ \\underline{\\otimes \\quad 239}&amp; \\\\ 84&amp; \\end{align*} &nbsp;\\)<\/p>\r\n\r\n<p>Let us define \\(\\otimes\\) to be left-associative, that is, \\(a \\otimes b \\otimes c\\) is to be interpreted as \\((a \\otimes b) \\otimes c\\).<\/p>\r\n\r\n<p>Given a binary operation \\(\\odot\\) and two non-negative integers \\(a\\) and \\(b\\), calculate the value of \\(a \\otimes (a + 1) \\otimes (a + 2) \\otimes \\dots \\otimes (b &minus; 1) \\otimes b\\).<\/p>\r\n","input":"<p>The first ten lines of the input file contain the description of the binary operation \\(\\odot\\). The \\(i\\)-th line of the input file contains a space-separated list of ten digits &mdash; the \\(j\\)-th digit in this list is equal to \\((i&minus;1) \\odot (j&minus;1)\\).<\/p>\r\n\r\n<p>The first digit in the first line is always 0.<\/p>\r\n\r\n<p>The eleventh line of the input file contains two non-negative integers \\(a\\) and \\(b\\) (0 &le; \\(a\\) &le; \\(b\\) &le; 10<sup>18<\/sup>).<\/p>\r\n","output":"<p>Output a single number &ndash; the value of \\(a \\otimes (a+ 1) \\otimes (a+ 2) \\otimes \\dots \\otimes (b&minus;1) \\otimes b\\) without extra leading zeroes.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]