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[Silver IV] Title: 초콜릿과 11과 팰린드롬, Time: 36 ms, Memory: 32412 KB -BaekjoonHub
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# [Silver IV] 초콜릿과 11과 팰린드롬 - 31460
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[문제 링크](https://www.acmicpc.net/problem/31460)
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### 성능 요약
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메모리: 32412 KB, 시간: 36 ms
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### 분류
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해 구성하기, 수학
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### 제출 일자
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2025년 4월 29일 21:59:45
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### 문제 설명
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<p>코코는 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$0$</span></mjx-container>부터 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c39"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$9$</span></mjx-container>까지의 숫자가 새겨진 초콜릿을 많이 갖고 있다. 코코는 이 초콜릿을 가지고 큰 수를 만들어서 한별이에게 선물하려고 한다.</p>
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<p>코코는 한별이가 팰린드롬 수, 특히 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$11$</span></mjx-container>을 좋아한다는 사실을 알고 있기 때문에, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$11$</span></mjx-container>의 배수인 팰린드롬 수를 만들고 싶다. 팰린드롬 수는 왼쪽에서 오른쪽으로 읽은 것과 오른쪽에서 왼쪽으로 읽은 것이 서로 같은 수를 말한다. 예를 들어, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c39"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$9$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$11$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c34"></mjx-c><mjx-c class="mjx-c37"></mjx-c><mjx-c class="mjx-c37"></mjx-c><mjx-c class="mjx-c34"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4774</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$4774$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c35"></mjx-c><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13531</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$13531$</span></mjx-container>은 팰린드롬 수이고, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c32"></mjx-c><mjx-c class="mjx-c33"></mjx-c><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1232</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1232$</span></mjx-container>, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1100</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$1100$</span></mjx-container>은 팰린드롬 수가 아니다.</p>
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<p>코코를 도와 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$11$</span></mjx-container>의 배수이면서 팰린드롬인 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>자리의 음이 아닌 정수를 하나 찾아주자. 각 숫자가 새겨진 초콜릿은 충분히 많다고 가정한다. <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$0$</span></mjx-container>을 제외한 수는 숫자 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$0$</span></mjx-container>으로 시작할 수 없다.</p>
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### 입력
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<p>첫 번째 줄에는 테스트 케이스의 개수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D447 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$T$</span></mjx-container>가 주어진다. <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D447 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>≤</mo><mi>T</mi><mo>≤</mo><mn>100</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$(1\le T\le 100)$</span> </mjx-container></p>
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<p>각 테스트 케이스에 대해, 양의 정수 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>이 한 줄에 주어진다. <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mo class="mjx-n"><mjx-c class="mjx-c28"></mjx-c></mjx-mo><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c></mjx-mn><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mi class="mjx-i" space="4"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c2264"></mjx-c></mjx-mo><mjx-mn class="mjx-n" space="4"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mstyle><mjx-mspace style="width: 0.167em;"></mjx-mspace></mjx-mstyle><mjx-mn class="mjx-n"><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c><mjx-c class="mjx-c30"></mjx-c></mjx-mn><mjx-mo class="mjx-n"><mjx-c class="mjx-c29"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mn>1</mn><mo>≤</mo><mi>N</mi><mo>≤</mo><mn>10</mn><mstyle scriptlevel="0"><mspace width="0.167em"></mspace></mstyle><mn>000</mn><mo stretchy="false">)</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$(1\le N\le 10\, 000)$</span> </mjx-container></p>
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### 출력
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<p>각 테스트 케이스에 대해, <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mn class="mjx-n"><mjx-c class="mjx-c31"></mjx-c><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>11</mn></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$11$</span></mjx-container>의 배수이면서 팰린드롬인 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$N$</span></mjx-container>자리의 음이 아닌 정수를 한 줄에 출력한다. 답이 여러 가지라면 아무거나 출력한다. 그러한 수가 없으면 <span style="color:#e74c3c;"><code>-1</code></span>을 대신 출력한다.</p>
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print(*[[0,'1'+'2'*(int(i)-2)+'1'][int(i)>1]for i in open(0)][1:])

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