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문제

상근이는 타일로 작품을 만드는 예술가이다. 크기가 N × N인 작품을 만들기 위해서 상근이는 1 × 1 타일을 사용한다. 색상은 빨강, 파랑, 노랑 중 하나이다. 작품은 가장 바깥쪽에 빨간색을 붙이고, 그 안쪽에 파란색을 붙이고, 그 안쪽에 노란색을 붙이는 방법으로 만든다. 이것을 N × N 정사각형이 가득 찰 때까지 반복한다. 타일 색은 바깥 쪽부터 순서대로 빨강, 파랑, 노랑, 빨강, 파랑, 노랑, ...이다.

상근이의 놀라운 미적 감각을 질투하는 창영이는 작품에 K개 타일을 제거했다. 상근이는 새로운 타일을 구입하여, 제거된 부분에 새로운 타일을 붙이려고 한다.

작품의 한 변의 크기 N, 창영이가 제거한 타일의 개수 K와 위치가 주어졌을 때, 제거된 타일의 색상을 구하는 프로그램을 작성하시오.

예를 들어, N = 11인 경우 상근이의 작품은 다음과 같다.

또, N = 16인 경우에는 아래와 같다.

입력

첫째 줄에 한 변의 길이 N이 주어진다. (1 ≤ N ≤ 109) 둘째 줄에는 창영이가 제거한 타일의 개수 K가 주어진다. (1 ≤ K ≤ 1000) 다음 줄부터 K개 줄에는 창영이가 제거한 타일의 위치 ai bi가 제거한 순서대로 주어진다. (1 ≤ ai ≤ N, 1 ≤ bi ≤ N) 타일은 왼쪽에서 ai번째, 위에서 bi번째에 있다. 같은 타일을 두 번 이상 제거하는 경우는 없다.

출력

창영이가 제거한 순서대로 타일의 색상을 출력한다. 빨간색은 1, 파란색은 2, 노란색은 3을 출력한다.

예제 입력 1

11
4
5 2
9 7
4 4
3 9

예제 출력 1

2
3
1
3

예제 입력 2

16
7
3 7
5 2
11 6
15 2
9 7
8 12
15 16

예제 출력 2

3
2
3
2
1
2
1

힌트

[{"problem_id":"5556","problem_lang":"0","title":"\ud0c0\uc77c","description":"<p>\uc0c1\uadfc\uc774\ub294 \ud0c0\uc77c\ub85c \uc791\ud488\uc744 \ub9cc\ub4dc\ub294 \uc608\uc220\uac00\uc774\ub2e4. \ud06c\uae30\uac00 N &times; N\uc778 \uc791\ud488\uc744 \ub9cc\ub4e4\uae30 \uc704\ud574\uc11c \uc0c1\uadfc\uc774\ub294 1 &times; 1 \ud0c0\uc77c\uc744 \uc0ac\uc6a9\ud55c\ub2e4. \uc0c9\uc0c1\uc740 \ube68\uac15, \ud30c\ub791, \ub178\ub791 \uc911 \ud558\ub098\uc774\ub2e4. \uc791\ud488\uc740 \uac00\uc7a5 \ubc14\uae65\ucabd\uc5d0 \ube68\uac04\uc0c9\uc744 \ubd99\uc774\uace0, \uadf8 \uc548\ucabd\uc5d0 \ud30c\ub780\uc0c9\uc744 \ubd99\uc774\uace0, \uadf8 \uc548\ucabd\uc5d0 \ub178\ub780\uc0c9\uc744 \ubd99\uc774\ub294 \ubc29\ubc95\uc73c\ub85c \ub9cc\ub4e0\ub2e4. \uc774\uac83\uc744 N &times; N \uc815\uc0ac\uac01\ud615\uc774 \uac00\ub4dd \ucc30 \ub54c\uae4c\uc9c0 \ubc18\ubcf5\ud55c\ub2e4. \ud0c0\uc77c \uc0c9\uc740 \ubc14\uae65 \ucabd\ubd80\ud130 \uc21c\uc11c\ub300\ub85c \ube68\uac15, \ud30c\ub791, \ub178\ub791, \ube68\uac15, \ud30c\ub791, \ub178\ub791, ...\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc0c1\uadfc\uc774\uc758 \ub180\ub77c\uc6b4 \ubbf8\uc801 \uac10\uac01\uc744 \uc9c8\ud22c\ud558\ub294 \ucc3d\uc601\uc774\ub294 \uc791\ud488\uc5d0 K\uac1c \ud0c0\uc77c\uc744 \uc81c\uac70\ud588\ub2e4. \uc0c1\uadfc\uc774\ub294 \uc0c8\ub85c\uc6b4 \ud0c0\uc77c\uc744 \uad6c\uc785\ud558\uc5ec, \uc81c\uac70\ub41c \ubd80\ubd84\uc5d0 \uc0c8\ub85c\uc6b4 \ud0c0\uc77c\uc744 \ubd99\uc774\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc791\ud488\uc758 \ud55c \ubcc0\uc758 \ud06c\uae30 N, \ucc3d\uc601\uc774\uac00 \uc81c\uac70\ud55c \ud0c0\uc77c\uc758 \uac1c\uc218 K\uc640 \uc704\uce58\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc81c\uac70\ub41c \ud0c0\uc77c\uc758 \uc0c9\uc0c1\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, N = 11\uc778 \uacbd\uc6b0 \uc0c1\uadfc\uc774\uc758 \uc791\ud488\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/artist1.png\" style=\"height:350px; width:350px\" \/><\/p>\r\n\r\n<p>\ub610, N = 16\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc544\ub798\uc640 \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/artist2.png\" style=\"height:510px; width:510px\" \/><\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud55c \ubcc0\uc758 \uae38\uc774 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; N &le; 10<sup>9<\/sup>) \ub458\uc9f8 \uc904\uc5d0\ub294 \ucc3d\uc601\uc774\uac00 \uc81c\uac70\ud55c \ud0c0\uc77c\uc758 \uac1c\uc218 K\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; K &le; 1000) \ub2e4\uc74c \uc904\ubd80\ud130 K\uac1c \uc904\uc5d0\ub294 \ucc3d\uc601\uc774\uac00 \uc81c\uac70\ud55c \ud0c0\uc77c\uc758 \uc704\uce58 a<sub>i<\/sub> b<sub>i<\/sub>\uac00 \uc81c\uac70\ud55c \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; a<sub>i<\/sub> &le; N, 1 &le; b<sub>i<\/sub> &le; N) \ud0c0\uc77c\uc740 \uc67c\ucabd\uc5d0\uc11c a<sub>i<\/sub>\ubc88\uc9f8, \uc704\uc5d0\uc11c b<sub>i<\/sub>\ubc88\uc9f8\uc5d0 \uc788\ub2e4. \uac19\uc740 \ud0c0\uc77c\uc744 \ub450 \ubc88 \uc774\uc0c1 \uc81c\uac70\ud558\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/p>\r\n","output":"<p>\ucc3d\uc601\uc774\uac00 \uc81c\uac70\ud55c \uc21c\uc11c\ub300\ub85c \ud0c0\uc77c\uc758 \uc0c9\uc0c1\uc744 \ucd9c\ub825\ud55c\ub2e4. \ube68\uac04\uc0c9\uc740 1, \ud30c\ub780\uc0c9\uc740 2, \ub178\ub780\uc0c9\uc740 3\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p><img alt=\"\" src=\"\/upload\/images\/artist3.png\" style=\"height:350px; width:350px\" \/><\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"5556","problem_lang":"2","title":"\u30bf\u30a4\u30eb (Tile)","description":"<p>JOI \u9ad8\u6821\u3067\u306f\uff0c 1 &times; 1 \u306e\u6b63\u65b9\u5f62\u306e\u30bf\u30a4\u30eb\u3092\u4f7f\u3063\u3066 N &times; N \u306e\u6b63\u65b9\u5f62\u306e\u58c1\u753b\u3092\u4f5c\u308a\uff0c \u6587\u5316\u796d\u3067\u5c55\u793a\u3059\u308b\u3053\u3068\u306b\u306a\u3063\u305f\uff0e \u30bf\u30a4\u30eb\u306e\u8272\u306f\uff0c\u8d64\uff0c\u9752\uff0c\u9ec4\u306e 3 \u7a2e\u985e\u3067\u3042\u308b\uff0e \u58c1\u753b\u306e\u30c7\u30b6\u30a4\u30f3\u306f\u6b21\u306e\u901a\u308a\u3067\u3042\u308b\uff0e \u307e\u305a\uff0c\u6700\u3082\u5916\u5074\u306e\u5468\u306b\u8d64\u306e\u30bf\u30a4\u30eb\u3092\u8cbc\u308a\uff0c\u305d\u306e\u5185\u5074\u306e\u5468\u306b\u9752\u306e\u30bf\u30a4\u30eb\u3092\u8cbc\u308b\uff0e \u3055\u3089\u306b\u305d\u306e\u5185\u5074\u306e\u5468\u306b\u9ec4\u8272\u306e\u30bf\u30a4\u30eb\u3092\u8cbc\u308b\uff0e \u3053\u308c\u3092 N &times; N \u306e\u6b63\u65b9\u5f62\u304c\u57cb\u3081\u5c3d\u304f\u3055\u308c\u308b\u307e\u3067\u7e70\u308a\u8fd4\u3059\uff0e \u7528\u3044\u308b\u30bf\u30a4\u30eb\u306e\u8272\u306f\uff0c \u4e00\u756a\u5916\u5074\u306e\u5468\u304b\u3089\u9806\u756a\u306b\u8d64\uff0c\u9752\uff0c\u9ec4\uff0c\u8d64\uff0c\u9752\uff0c\u9ec4\uff0c&hellip;\u3067\u3042\u308b\uff0e<\/p>\r\n\r\n<p>\u6587\u5316\u796d\u304c\u8fd1\u3065\u3044\u3066\u304d\u305f\u3042\u308b\u65e5\uff0c \u58c1\u753b\u306e\u3046\u3061 K \u679a\u306e\u30bf\u30a4\u30eb\u304c\u306f\u304c\u308c\u3066\u3044\u308b\u3053\u3068\u304c\u5224\u660e\u3057\u305f\uff0e \u305d\u3053\u3067\uff0c\u65b0\u3057\u3044\u30bf\u30a4\u30eb\u3092\u8cfc\u5165\u3057\u3066\uff0c\u306f\u304c\u308c\u305f\u7b87\u6240\u306b\u65b0\u3057\u3044\u30bf\u30a4\u30eb\u3092\u8cbc\u308b\u3053\u3068\u306b\u3057\u305f\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u3068\u3057\u3066\u58c1\u753b\u306e\u4e00\u8fba\u306e\u9577\u3055 N \u3068\uff0c \u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u306e\u679a\u6570 K\uff0c K \u679a\u306e\u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u306e\u4f4d\u7f6e\u304c\u4e0e\u3048\u3089\u308c\u305f\u3068\u304d\uff0c \u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u306e\u8272\u3092\u6c42\u3081\u308b\u30d7\u30ed\u30b0\u30e9\u30e0\u3092\u4f5c\u6210\u305b\u3088\uff0e<\/p>\r\n\r\n<p>\u4f8b\u3048\u3070\uff0cN = 11 \u306e\u5834\u5408\uff0c11 &times; 11 \u306e\u58c1\u753b\u306e\u30c7\u30b6\u30a4\u30f3\u306f\u4e0b\u56f3\u306e\u901a\u308a\u3067\u3042\u308b\uff0e&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/artist1.png\" style=\"height:350px; width:350px\" \/><\/p>\r\n\r\n<p>\u307e\u305f\uff0cN = 16 \u306e\u5834\u5408\uff0c16 &times; 16 \u306e\u58c1\u753b\u306e\u30c7\u30b6\u30a4\u30f3\u306f\u4e0b\u56f3\u306e\u901a\u308a\u3067\u3042\u308b\uff0e&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/artist2.png\" style=\"height:510px; width:510px\" \/><\/p>\r\n","input":"<p>\u5165\u529b\u306f\u5168\u90e8\u3067 2+K \u884c\u304b\u3089\u306a\u308b\uff0e 1 \u884c\u76ee\u306b\u306f\uff0c\u58c1\u753b\u306e\u4e00\u8fba\u306e\u9577\u3055 N \uff081 \u2266 N \u2266 1000000000 = 10<sup>9<\/sup>\uff09\u304c\uff0c 2 \u884c\u76ee\u306b\u306f\uff0c\u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u306e\u679a\u6570 K \uff081 \u2266 K \u2266 1000\uff09\u304c\u66f8\u304b\u308c\u3066\u3044\u308b\uff0e 2+i \u884c\u76ee\uff081 \u2266 i \u2266 K\uff09\u306b\u306f\uff0c2 \u3064\u306e\u6574\u6570 a<sub>i<\/sub> \u3068 b<sub>i<\/sub> \uff081 \u2266 a<sub>i<\/sub> \u2266 N, 1 \u2266 b<sub>i<\/sub> \u2266 N\uff09\u304c\u7a7a\u767d\u533a\u5207\u308a\u3067\u66f8\u304b\u308c\u3066\u304a\u308a\uff0c i \u679a\u76ee\u306e\u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u304c\uff0c \u5de6\u304b\u3089 ai \u5217\u76ee\uff0c\u4e0a\u304b\u3089 bi \u884c\u76ee\u306e\u30bf\u30a4\u30eb\u3067\u3042\u308b\u3053\u3068\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p>\u5165\u529b\u306e 3 \u884c\u76ee\u304b\u3089 2+K \u884c\u76ee\u306b\u306f\u540c\u3058\u30bf\u30a4\u30eb\u3092\u8868\u3059\u884c\u304c\u91cd\u8907\u3057\u3066\u73fe\u308c\u308b\u3053\u3068\u306f\u306a\u3044\uff0e&nbsp;<\/p>\r\n","output":"<p>\u51fa\u529b\u306f K \u884c\u304b\u3089\u306a\u308b\uff0e \u5404\u884c\u306f 1 \u3064\u306e\u6574\u6570\u304b\u3089\u306a\u308a\uff0c i \u884c\u76ee\uff081 \u2266 i \u2266 K\uff09\u306e\u6574\u6570\u306f\uff0ci \u679a\u76ee\u306e\u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u304c\u8d64\u306e\u3068\u304d\u306f 1 \u3092\uff0c\u9752\u306e\u3068\u304d\u306f 2 \u3092\uff0c\u9ec4\u8272\u306e\u3068\u304d\u306f 3 \u3092\u8868\u3059\uff0e<\/p>\r\n","hint":"<p>\u5165\u529b\u4f8b 1 \u306b\u304a\u3044\u3066\uff0c11 &times; 11 \u306e\u58c1\u753b\u306f\u4ee5\u4e0b\u306e\u56f3\u306e\u901a\u308a\u3067\u3042\u308b\uff0e \u300c&times;\u300d\u306f\uff0c\u306f\u304c\u308c\u305f\u30bf\u30a4\u30eb\u3092\u8868\u3059\uff0e<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/artist3.png\" style=\"height:350px; width:350px\" \/><\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Japanese"}]