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[Bronze I] Title: 더블팰린드롬, Time: 160 ms, Memory: 34536 KB -BaekjoonHub
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‎백준/Bronze/32357. 더블팰린드롬/README.md‎

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# [Bronze I] 더블팰린드롬 - 32357
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[문제 링크](https://www.acmicpc.net/problem/32357)
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### 성능 요약
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메모리: 34536 KB, 시간: 160 ms
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### 분류
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애드 혹, 구현, 수학, 문자열
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### 제출 일자
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2025년 4월 30일 20:20:41
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### 문제 설명
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<p>종현은 알고리즘 과제로 팰린드롬에 대해서 공부하고 있다. 팰린드롬(palindrome)이란 앞에서부터 읽으나 뒤에서부터 읽으나 같은 문자열을 말한다. 예를 들어 'abba', 'level' 등은 팰린드롬이며 'abab', 'boj' 등은 팰린드롬이 아니다.</p>
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<p>종현은 팰린드롬을 보다가 새로운 현상을 발견하게 되었다. 먼저, 길이가 짝수인 문자열 <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-c1D44B 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>X</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X$</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-mi class="mjx-i"><mjx-c class="mjx-c1D44C 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>Y</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Y$</span></mjx-container>를 고른다. 그리고 <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-c1D44B 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>X</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X$</span></mjx-container>를 같은 길이의 두 부분으로 나누어 문자열 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44B TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.024em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>1</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X_1$</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-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44B TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.024em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>2</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X_2$</span></mjx-container>를 얻는다. 다음으로 종현은 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44B TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.024em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>1</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X_1$</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-mi class="mjx-i"><mjx-c class="mjx-c1D44C 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>Y</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Y$</span></mjx-container>와 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D44B TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em; margin-left: -0.024em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>X</mi><mn>2</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X_2$</span></mjx-container>를 순서대로 이어 붙여 새로운 문자열 <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-c1D44D 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>Z</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Z$</span></mjx-container>를 얻는다. 이렇게 얻은 <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-c1D44D 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>Z</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Z$</span></mjx-container>가 팰린드롬이라면 종현은 <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-c1D44B 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>X</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X$</span></mjx-container>와 <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-c1D44C 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>Y</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Y$</span></mjx-container>가 <strong>더블팰린드롬 현상</strong>을 일으킨다고 부르기로 했다.</p>
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<p style="text-align: center;"><img alt="" src="https://upload.acmicpc.net/cce0e223-82fa-4aec-8d55-fe08e95d307c/-/preview/" style="height: 40%; width: 50%;"></p>
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<p>길이가 짝수인 <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>개의 서로 다른 문자열 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_1$</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-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_2$</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-mo class="mjx-n"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$...$</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-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mi>N</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_N$</span></mjx-container>이 주어질 때, <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-c1D44B TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-msub space="4"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>X</mi><mo>=</mo><msub><mi>s</mi><mi>i</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$X=s_i$</span></mjx-container>와 <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-c1D44C TEX-I"></mjx-c></mjx-mi><mjx-mo class="mjx-n" space="4"><mjx-c class="mjx-c3D"></mjx-c></mjx-mo><mjx-msub space="4"><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D457 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Y</mi><mo>=</mo><msub><mi>s</mi><mi>j</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$Y=s_j$</span></mjx-container>가 <strong>더블팰린드롬 현상</strong>을 일으키게 하는 두 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-c1D456 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>i</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$i$</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-mi class="mjx-i"><mjx-c class="mjx-c1D457 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>j</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$j$</span></mjx-container>의 쌍 <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-mi class="mjx-i"><mjx-c class="mjx-c1D456 TEX-I"></mjx-c></mjx-mi></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo stretchy="false">(</mo><mi>i</mi></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$(i$</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-mi class="mjx-i"><mjx-c class="mjx-c1D457 TEX-I"></mjx-c></mjx-mi><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"><mi>j</mi><mo stretchy="false">)</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$j)$</span></mjx-container>의 개수를 구해보자. </p>
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### 입력
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<p>첫 번째 줄에 문자열의 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-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 주어진다.</p>
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<p>두 번째 줄부터 <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>개의 줄에 걸쳐 길이가 짝수인 알파벳 소문자로만 구성된 문자열 <mjx-container class="MathJax" jax="CHTML" style="font-size: 104.6%; position: relative;"><mjx-math class="MJX-TEX" aria-hidden="true"><mjx-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c31"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>1</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_1$</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-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mn class="mjx-n" size="s"><mjx-c class="mjx-c32"></mjx-c></mjx-mn></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mn>2</mn></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_2$</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-mo class="mjx-n"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo><mjx-mo class="mjx-n" space="2"><mjx-c class="mjx-c2E"></mjx-c></mjx-mo></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$...$</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-msub><mjx-mi class="mjx-i"><mjx-c class="mjx-c1D460 TEX-I"></mjx-c></mjx-mi><mjx-script style="vertical-align: -0.15em;"><mjx-mi class="mjx-i" size="s"><mjx-c class="mjx-c1D441 TEX-I"></mjx-c></mjx-mi></mjx-script></mjx-msub></mjx-math><mjx-assistive-mml unselectable="on" display="inline"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>s</mi><mi>N</mi></msub></math></mjx-assistive-mml><span aria-hidden="true" class="no-mathjax mjx-copytext">$s_N$</span></mjx-container>이 주어진다.</p>
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### 출력
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<p>더블팰린드롬 현상을 일으킬 수 있는 쌍의 개수를 출력한다.</p>
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‎백준/Bronze/32357. 더블팰린드롬/더블팰린드롬.py‎

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# 32357 더블팰린드롬
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# 브론즈 1
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import sys, math
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input = sys.stdin.readline
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# 문자열의 개수
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n = int(input())
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palin = 0
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for _ in range(n):
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s = input().strip()
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# 팰린드롬이면
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if list(s[:len(s)//2]) == list(reversed(s[len(s)//2:])):
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palin += 1
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print(math.perm(palin, 2))
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#math.perm(n, r)
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#순서를 고려하여 n개중 r개만큼 선택하는 경우의 수 (순열)
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#math.comb(n, r)
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#순서에 상관없이 n개중 r개만큼 선택하는 경우의 수 (조합)

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