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문제

Albert가 다니는 회사의 주차장에 지금 자동차 n대 일렬로 (좌에서 우로) 주차되어있다. 편의상 차는 좌측부터 순서대로 1번에서 n번까지 번호로 나타내자. i번 차의 번호판에 적힌 문자열을 x[i]라 하자. n개의 문자열은 서로 다르며, 영어 대/소문자 (a-z와 A-Z)로만 구성된 길이 k인 문자열이다. 즉, 모든 번호판의 길이는 같다.

임의의 두 자동차 i, j 에 대하여 번호판 x[i] 와 x[j]가 아래 조건을 모두 만족하면 두 자동차는 비슷한 번호판을 가졌다고 한다:

  • 26가지의 각 알파벳에 대하여, 대/소문자를 무시했을 때 해당 알파벳이 x[i]에 적힌 횟수와 x[j]에 적힌 횟수가 같다 (이 조건은 각 알파벳에 대해 만족해야 한다).
  • x[i]에 적힌 대문자의 개수와 x[j]에 적힌 대문자의 개수가 같다.

예를 들어, n = 4, k = 3 이고 x = ["AtY", "YtA", "aTy", "Ayt"]라 하자.

  • 1번차와 2번차의 번호판은 비슷하다: 두 번호판 모두 A/a 1개, T/t 1개, Y/y 1개씩을 포함하고 대문자는 3글자 중 2글자이다.
  • 3번차와 4번차의 번호판은 비슷하다: 두 번호판 모두 A/a 1개, T/t 1개, Y/y 1개씩을 포함하고 대문자는 3글자 중 1글자이다.
  • 1번차와 3번차의 번호판은 비슷하지 않다: 1번차는 대문자 2개, 3번차는 대문자 1개를 포함한다 (단, 첫 번째 조건은 만족한다).

입력으로 n, k 그리고 x[1], ..., x[n]이 주어졌을 때, 비슷한 번호판 쌍의 수를 구해서 Albert에게 알려주자.

입력

첫 줄에 테스트 케이스의 수 T가 주어진다.

각 테스트 케이스의 첫 줄에는 n과 k개 공백으로 구분되어 주어진다.

두 번째 줄에는 길이가 k인 문자열 n개가 공백으로 구분되어 주어진다.

출력

각 테스트 케이스의 정답을 각 줄에 출력한다.

제한

  • 1 ≤ T ≤ 20
  • 1 ≤ n ≤ 10,000
  • 1 ≤ k ≤ 20

예제 입력 1

5
4 3
AtY YtA aTy Ayt
4 4
AAaa AaAa aaAA AaaA
5 4
AAAA aaaa AAaa AAAa Aaaa
10 1
A a B b C c D d E e
2 10
ABCDEabcde abcdeEDCBA

예제 출력 1

2
6
0
0
1

예제 1: 본문에서 다루었다.

예제 2: 모든 여섯 쌍의 번호판이 서로 비슷하다.

예제 3: 각 번호판에 적힌 영문 대문자의 개수가 다르므로 비슷한 번호판 쌍이 존재하지 않는다.

예제 4: 추가 설명 없음

예제 5: 추가 설명 없음

[{"problem_id":"21980","problem_lang":"0","title":"\ube44\uc2b7\ud55c \ubc88\ud638\ud310","description":"<p>Albert\uac00 \ub2e4\ub2c8\ub294 \ud68c\uc0ac\uc758 \uc8fc\ucc28\uc7a5\uc5d0 \uc9c0\uae08 \uc790\ub3d9\ucc28 n\ub300 \uc77c\ub82c\ub85c (\uc88c\uc5d0\uc11c \uc6b0\ub85c) \uc8fc\ucc28\ub418\uc5b4\uc788\ub2e4. \ud3b8\uc758\uc0c1 \ucc28\ub294 \uc88c\uce21\ubd80\ud130 \uc21c\uc11c\ub300\ub85c 1\ubc88\uc5d0\uc11c n\ubc88\uae4c\uc9c0 \ubc88\ud638\ub85c \ub098\ud0c0\ub0b4\uc790. i\ubc88 \ucc28\uc758 \ubc88\ud638\ud310\uc5d0 \uc801\ud78c \ubb38\uc790\uc5f4\uc744 x[i]\ub77c \ud558\uc790. n\uac1c\uc758 \ubb38\uc790\uc5f4\uc740 \uc11c\ub85c \ub2e4\ub974\uba70, \uc601\uc5b4 \ub300\/\uc18c\ubb38\uc790 (a-z\uc640 A-Z)\ub85c\ub9cc \uad6c\uc131\ub41c \uae38\uc774 k\uc778 \ubb38\uc790\uc5f4\uc774\ub2e4. \uc989, \ubaa8\ub4e0 \ubc88\ud638\ud310\uc758 \uae38\uc774\ub294 \uac19\ub2e4.<\/p>\r\n\r\n<p>\uc784\uc758\uc758 \ub450 \uc790\ub3d9\ucc28 i, j \uc5d0 \ub300\ud558\uc5ec \ubc88\ud638\ud310 x[i] \uc640 x[j]\uac00 \uc544\ub798 \uc870\uac74\uc744 \ubaa8\ub450 \ub9cc\uc871\ud558\uba74 \ub450 \uc790\ub3d9\ucc28\ub294 \ube44\uc2b7\ud55c \ubc88\ud638\ud310\uc744 \uac00\uc84c\ub2e4\uace0 \ud55c\ub2e4:<\/p>\r\n\r\n<ul>\r\n\t<li>26\uac00\uc9c0\uc758 \uac01 \uc54c\ud30c\ubcb3\uc5d0 \ub300\ud558\uc5ec, \ub300\/\uc18c\ubb38\uc790\ub97c \ubb34\uc2dc\ud588\uc744 \ub54c \ud574\ub2f9 \uc54c\ud30c\ubcb3\uc774 x[i]\uc5d0 \uc801\ud78c \ud69f\uc218\uc640 x[j]\uc5d0 \uc801\ud78c \ud69f\uc218\uac00 \uac19\ub2e4 (\uc774 \uc870\uac74\uc740 \uac01 \uc54c\ud30c\ubcb3\uc5d0 \ub300\ud574 \ub9cc\uc871\ud574\uc57c \ud55c\ub2e4).<\/li>\r\n\t<li>x[i]\uc5d0 \uc801\ud78c \ub300\ubb38\uc790\uc758 \uac1c\uc218\uc640 x[j]\uc5d0 \uc801\ud78c \ub300\ubb38\uc790\uc758 \uac1c\uc218\uac00 \uac19\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, n = 4, k = 3 \uc774\uace0 x = [&quot;AtY&quot;, &quot;YtA&quot;, &quot;aTy&quot;, &quot;Ayt&quot;]\ub77c \ud558\uc790.<\/p>\r\n\r\n<ul>\r\n\t<li>1\ubc88\ucc28\uc640 2\ubc88\ucc28\uc758 \ubc88\ud638\ud310\uc740 \ube44\uc2b7\ud558\ub2e4: \ub450 \ubc88\ud638\ud310 \ubaa8\ub450 A\/a 1\uac1c, T\/t 1\uac1c, Y\/y 1\uac1c\uc529\uc744 \ud3ec\ud568\ud558\uace0 \ub300\ubb38\uc790\ub294 3\uae00\uc790 \uc911 2\uae00\uc790\uc774\ub2e4.<\/li>\r\n\t<li>3\ubc88\ucc28\uc640 4\ubc88\ucc28\uc758 \ubc88\ud638\ud310\uc740 \ube44\uc2b7\ud558\ub2e4: \ub450 \ubc88\ud638\ud310 \ubaa8\ub450 A\/a 1\uac1c, T\/t 1\uac1c, Y\/y 1\uac1c\uc529\uc744 \ud3ec\ud568\ud558\uace0 \ub300\ubb38\uc790\ub294 3\uae00\uc790 \uc911 1\uae00\uc790\uc774\ub2e4.<\/li>\r\n\t<li>1\ubc88\ucc28\uc640 3\ubc88\ucc28\uc758 \ubc88\ud638\ud310\uc740 \ube44\uc2b7\ud558\uc9c0 \uc54a\ub2e4: 1\ubc88\ucc28\ub294 \ub300\ubb38\uc790 2\uac1c, 3\ubc88\ucc28\ub294 \ub300\ubb38\uc790 1\uac1c\ub97c \ud3ec\ud568\ud55c\ub2e4 (\ub2e8, \uccab \ubc88\uc9f8 \uc870\uac74\uc740 \ub9cc\uc871\ud55c\ub2e4).<\/li>\r\n<\/ul>\r\n\r\n<p>\uc785\ub825\uc73c\ub85c n, k \uadf8\ub9ac\uace0 x[1], ..., x[n]\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ube44\uc2b7\ud55c \ubc88\ud638\ud310 \uc30d\uc758 \uc218\ub97c \uad6c\ud574\uc11c Albert\uc5d0\uac8c \uc54c\ub824\uc8fc\uc790.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d0\ub294 n\uacfc k\uac1c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uae38\uc774\uac00 k\uc778 \ubb38\uc790\uc5f4 n\uac1c\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc815\ub2f5\uc744 \uac01 \uc904\uc5d0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>1 &le; T &le; 20<\/li>\r\n\t<li>1 &le; n &le; 10,000<\/li>\r\n\t<li>1 &le; k &le; 20<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>\uc608\uc81c 1: \ubcf8\ubb38\uc5d0\uc11c \ub2e4\ub8e8\uc5c8\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 2: \ubaa8\ub4e0 \uc5ec\uc12f \uc30d\uc758 \ubc88\ud638\ud310\uc774 \uc11c\ub85c \ube44\uc2b7\ud558\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 3: \uac01 \ubc88\ud638\ud310\uc5d0 \uc801\ud78c \uc601\ubb38 \ub300\ubb38\uc790\uc758 \uac1c\uc218\uac00 \ub2e4\ub974\ubbc0\ub85c \ube44\uc2b7\ud55c \ubc88\ud638\ud310 \uc30d\uc774 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n\r\n<p>\uc608\uc81c 4: \ucd94\uac00 \uc124\uba85 \uc5c6\uc74c<\/p>\r\n\r\n<p>\uc608\uc81c 5: \ucd94\uac00 \uc124\uba85 \uc5c6\uc74c<\/p>\r\n"},{"problem_id":"21980","problem_lang":"1","title":"Car License Plates","description":"<p>Albert sees n cars (from left to right) parked in a parking lot (for convenience, cars are numbered from 1 to n). Let x[i] be the i-th car&#39;s license plate. These n strings are distinct, and each only consists of exactly k&nbsp;English letters (&#39;a&#39;-&#39;z&#39; and &#39;A&#39;-&#39;Z&#39;) -- that is, license plates have the same-length strings.<\/p>\r\n\r\n<p>For any two cars i and j, if their license plates x[i] and x[j] satisfy the following, then we say their plates are similar:<\/p>\r\n\r\n<ul>\r\n\t<li>For each of the 26 English alphabet, the number of occurrences of the alphabet (if we ignore the letter case) in x[i] is the same as the number in x[j] (this condition must be met for each alphabet).<\/li>\r\n\t<li>The number of uppercase alphabets in x[i] is the same as the number in x[j].<\/li>\r\n<\/ul>\r\n\r\n<p>For instance, let n = 4, k = 3, and x = [&quot;AtY&quot;, &quot;YtA&quot;, &quot;aTy&quot;, &quot;Ayt&quot;].<\/p>\r\n\r\n<ul>\r\n\t<li>1st car and 2nd car&#39;s plates are similar: Both have one A\/a, one T\/t, and one Y\/y, among which two are uppercase alphabets.<\/li>\r\n\t<li>3rd car and 4th car&#39;s plates are similar: Both have one A\/a, one T\/t, and one Y\/y, among which one is an uppercase alphabet.&nbsp;<\/li>\r\n\t<li>1st car and 3rd car&#39;s plates are not similar: x[1] contains two uppercase alphabets and x[3] contains one uppercase alphabet (yet, the first condition on alphabets is satisfied).<\/li>\r\n<\/ul>\r\n\r\n<p>Given n, k, and x[1], ..., x[n], let Albert help count the number of similar car plate pairs.<\/p>\r\n","input":"<p>The first line of the input will contain a number, T, the number of test cases.<\/p>\r\n\r\n<p>For each test case, the first line will contain n and k, separated by whitespace.<\/p>\r\n\r\n<p>The second line of each test case will contain n strings of length k each, separated by whitespace.<\/p>\r\n","output":"<p>For each test case, output the answer in a single line.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>1 &le; T &le; 20<\/li>\r\n\t<li>1 &le; n &le; 10,000<\/li>\r\n\t<li>1 &le; k &le; 20<\/li>\r\n<\/ul>\r\n","sample_explain_1":"<p>Case 1: Discussed in the problem statement.<\/p>\r\n\r\n<p>Case 2: All pairs of plates are similar.<\/p>\r\n\r\n<p>Case 3: Plates contain&nbsp;different numbers of&nbsp;uppercase letters, and therefore no similar plates exist.<\/p>\r\n\r\n<p>Case 4: No explanation provided.<\/p>\r\n\r\n<p>Case 5: No explanation provided.<\/p>\r\n"}]

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