Split (1)

train · 39.1k rows

task stringlengths 0 154k	__index_level_0__ int64 0 39.2k
Score : 100 points Problem Statement Takahashi wants to print a document with N pages double-sided, where two pages of data can be printed on one sheet of paper. At least how many sheets of paper does he need? Constraints N is an integer. 1 \leq N \leq 100 Input Input is given from Standard Input in the following format: N Output Print the answer. Sample Input 1 5 Sample Output 1 3 By printing the 1 -st, 2 -nd pages on the 1 -st sheet, 3 -rd and 4 -th pages on the 2 -nd sheet, and 5 -th page on the 3 -rd sheet, we can print all the data on 3 sheets of paper. Sample Input 2 2 Sample Output 2 1 Sample Input 3 100 Sample Output 3 50	36,101
E: Arai's - Arai's - 問題スクールアイドル時代から、国民的人気を誇ってきた女性アイドルグループArai's。今では、たくさんの「あらい」さんが所属する大規模なグループとして、世界レベルで活躍している。そして今日、新たなるプロジェクトの始動が決定した。彼女たちは、小さなユニットをいくつか結成することで、さらなる売上の向上を試みることになったのである。 Arai'sには「荒井」さんが A 人，「新井」さんが B 人在籍しており、合計で A+B 人の「あらい」さんからなる。新ユニットは、「荒井」さん一人と「新井」さん一人のペアで構成する。（ここで、同じ「あらい」さんが複数のユニットに所属していはいけない。）ただし、ある「荒井」さんが一部の「新井」さんのことを良く思っていないうえに、同様にある「新井」さんが一部の「荒井」さんのことを良く思っていない。「あらい」さんたちはユニットを組む際に、良く思っていない「あらい」さんをペアとして認めてくれず、一方でも認めてくれなければユニットを組むことはできない。 Arai'sのマネージャーであるあなたは、なるべくたくさんのユニットを作りたいと考えているが、メンバーの交友関係からその限界を感じていた。そこであなたは、「あらい」さんたちと個別に面談し、ユニットを組ませたい「あらい」さんについての、良い噂を聞かせることを考えた。面談をした「あらい」さんは、噂に聞いた「あらい」さんを見直し、ユニットのペアとして認めるようになる。しかし、あなたはそれほど時間をとることができないため、最大 K 回までしか噂を聞かせることができない。あなたは限られた時間の中で、結成できるユニットの数を最大化しようと試みた。あなたが結成できるユニットの数の最大値を求めよ。入力形式 A B K a_1 ... a_A b_1 ... b_B 1行目には、「荒井」さんの人数 A と「新井」さんの人数 B ( 1 \≤ A, B \≤ 200 であり A , B は整数)、噂を聞かせることができる人数 K ( 0 \≤ K \≤ 200 であり K は整数)が空白区切りで与えられる。続く A 行には、それぞれ長さ B の 0 と 1 のみからなる文字列が与えられる。そのうち i 行目の文字列 a_i の j 文字目が 1 であるとき、 i 番目の「荒井」さんは j 番目の「新井」さんを良く思っていない。続く B 行には、それぞれ長さ A の 0 と 1 のみからなる文字列が与えられる。そのうち i 行目の文字列 b_i の j 文字目が 1 であるとき、 i 番目の「新井」さんは j 番目の「荒井」さんを良く思っていない。出力形式あなたが結成できるユニット数の最大値を1行に出力せよ。入力例1 3 3 4 111 111 111 111 111 111 出力例1 2 入力例2 3 3 2 101 100 010 001 011 111 出力例2 3 入力例3 5 6 3 101101 110110 010111 110110 110111 01010 10101 11101 01011 11011 11011 出力例3 4	36,102
Score : 900 points Problem Statement Snuke has a sequence p , which is a permutation of (0,1,2, ...,N-1) . The i -th element ( 0 -indexed) in p is p_i . He can perform N-1 kinds of operations labeled 1,2,...,N-1 any number of times in any order. When the operation labeled k is executed, the procedure represented by the following code will be performed: for(int i=k;i<N;i++) swap(p[i],p[i-k]); He would like to sort p in increasing order using between 0 and 10^{5} operations (inclusive). Show one such sequence of operations. It can be proved that there always exists such a sequence of operations under the constraints in this problem. Constraints 2 \leq N \leq 200 0 \leq p_i \leq N-1 p is a permutation of (0,1,2,...,N-1) . Partial Scores In the test set worth 300 points, N \leq 7 . In the test set worth another 400 points, N \leq 30 . Input Input is given from Standard Input in the following format: N p_0 p_1 ... p_{N-1} Output Let m be the number of operations in your solution. In the first line, print m . In the i -th of the following m lines, print the label of the i -th executed operation. The solution will be accepted if m is at most 10^5 and p is in increasing order after the execution of the m operations. Sample Input 1 5 4 2 0 1 3 Sample Output 1 4 2 3 1 2 Each operation changes p as shown below: Sample Input 2 9 1 0 4 3 5 6 2 8 7 Sample Output 2 11 3 6 1 3 5 2 4 7 8 6 3	36,103
F - Acceleration of Network インターネットと言う広大な海は少しずつ黒く塗りつぶされていった。ボットの反乱、DDOS攻撃の嵐、ウィルスの蔓延、何度も何度も繰り返されたクラッカーとの戦争で、人もインターネットもボロボロになった。人の手では、インターネットはどうにもならない。だから人は、とんでもない時間をかけてインターネットを復旧できる「少女」を造った。少女は、インターネットの手当をはじめた。果てしなく広いインターネットの世界をどうにかしようと頑張った。まだ少女ひとりでは撚り対線を織る事くらいしかできないけど、長い長い時がすぎてインターネットが少し復旧すれば、みんなと一緒に頑張れるだろうという期待をこめて。問題文少女はかつてインターネットに存在した N 個のサービスを復旧するために日々頑張っている．現在を 0 日目とする．インターネットがどの程度復旧しているかを復旧度という指標で表し，現在の復旧度は 0 であるとする．少女は毎日作業をし，復旧度を 1 日につき 1 ずつ上げていく．任意のまだ復旧していないサービス i は，復旧度が w i 以上になると自動的に復旧する．サービス i が復旧すると，みんなが手伝ってくれることにより，復旧した次の日から x i 日間だけ作業がはかどり，復旧度の増加が加速する．サービスには 3 つの種類があり，種類によって復旧度がどの程度増加するのかが異なる．サービスの種類を 0, 1, 2 の番号で表すとする．サービス i の種類を t i (∈ {0, 1, 2}) とすると，サービス i が復旧してから d-1 日目から d 日目にかけて (1 ≤ d ≤ x i ) ， t i =0 の場合は 1 ， t i =1 の場合は d ，そして t i =2 の場合は d 2 だけ，少女の作業とは別に復旧度が増加する．また，同時に複数のサービスが復旧している場合，それぞれのサービスは独立に並行して復旧度を増加させる．少女はサービスが復旧するまでにとんでもない時間がかかると思ったので，現在から何日目にサービスが復旧するか調べることにした．またある日にち y j に復旧度がいくらになっているかも気になったので，それも Q 日分だけ調べることにした．入力形式入力は以下の形式で与えられる． N Q w 1 t 1 x 1 ... w N t N x N y 1 ... y Q 出力形式最初に N 行出力し， i 行目にはサービス i の復旧する日にちを出力せよ．次に Q 行出力し， j 行目には y j 日目に復旧度がいくらになっているかを出力せよ．サービスが復旧する日にちが 3,652,425 を超える場合は Many years later と出力せよ．制約 0 ≤ N ≤ 10 5 1 ≤ Q ≤ 10 5 0 ≤ w i < 2 60 w i ≤ w i+1 (1 ≤ i < N) t i ∈ {0, 1, 2} 1 ≤ x i ≤ 10 4 0 ≤ y j ≤ 3,652,425 y j < y j+1 (1 ≤ j < Q) 入力値はすべて整数である．この問題の判定には，15 点分のテストケースのグループが設定されている．このグループに含まれるテストケースは上記の制約に加えて下記の制約も満たす． N,Q,w i ,y j ≤ 1,000 注意 0 日目の復旧度は 0 である． w i =0 の時，サービス i は 0 日目に復旧する．入出力例入力例1 3 11 1 0 2 4 1 3 7 2 4 0 1 2 3 4 5 6 7 8 9 10 出力例1 1 3 4 0 1 3 5 7 11 19 29 46 47 48 入力例2 5 5 10000 0 20 10000 1 30 10000 0 40 10000 2 70 30000 2 10000 5000 10000 15000 20000 25000 出力例2 10000 10000 10000 10000 10039 5000 10000 40711690801 329498273301 333383477320 入力例3 2 2 3652425 0 1 3652426 2 10000 3652424 3652425 出力例3 3652425 Many years later 3652424 3652425 2つ目のサービスは復旧する日にちが 3,652,425 日を超えているので Many years later と出力している． Writer : 森槙悟 Tester : 田村和範	36,104
Score : 400 points Problem Statement There are N pieces of sushi. Each piece has two parameters: "kind of topping" t_i and "deliciousness" d_i . You are choosing K among these N pieces to eat. Your "satisfaction" here will be calculated as follows: The satisfaction is the sum of the "base total deliciousness" and the "variety bonus". The base total deliciousness is the sum of the deliciousness of the pieces you eat. The variety bonus is xx , where x is the number of different kinds of toppings of the pieces you eat. You want to have as much satisfaction as possible. Find this maximum satisfaction. Constraints 1 \leq K \leq N \leq 10^5 1 \leq t_i \leq N 1 \leq d_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N K t_1 d_1 t_2 d_2 . . . t_N d_N Output Print the maximum satisfaction that you can obtain. Sample Input 1 5 3 1 9 1 7 2 6 2 5 3 1 Sample Output 1 26 If you eat Sushi 1,2 and 3 : The base total deliciousness is 9+7+6=22 . The variety bonus is 22=4 . Thus, your satisfaction will be 26 , which is optimal. Sample Input 2 7 4 1 1 2 1 3 1 4 6 4 5 4 5 4 5 Sample Output 2 25 It is optimal to eat Sushi 1,2,3 and 4 . Sample Input 3 6 5 5 1000000000 2 990000000 3 980000000 6 970000000 6 960000000 4 950000000 Sample Output 3 4900000016 Note that the output may not fit into a 32 -bit integer type.	36,105
Problem E: Optimal Rest Music Macro Language (MML) is a language for textual representation of musical scores. Although there are various dialects of MML, all of them provide a set of commands to describe scores, such as commands for notes, rests, octaves, volumes, and so forth. In this problem, we focus on rests, i.e. intervals of silence. Each rest command consists of a command specifier ‘R’ followed by a duration specifier. Each duration specifier is basically one of the following numbers: ‘1’, ‘2’, ‘4’, ‘8’, ‘16’, ‘32’, and ‘64’, where ‘1’ denotes a whole (1), ‘2’ a half (1/2), ‘4’ a quarter (1/4), ‘8’ an eighth (1/8), and so on. This number is called the base duration, and optionally followed by one or more dots. The first dot adds the duration by the half of the base duration. For example, ‘4.’ denotes the duration of ‘4’ (a quarter) plus ‘8’ (an eighth, i.e. the half of a quarter), or simply 1.5 times as long as ‘4’. In other words, ‘R4.’ is equivalent to ‘R4R8’. In case with two or more dots, each extra dot extends the duration by the half of the previous one. Thus ‘4..’ denotes the duration of ‘4’ plus ‘8’ plus ‘16’, ‘4...’ denotes the duration of ‘4’ plus ‘8’ plus ‘16’ plus ‘32’, and so on. The duration extended by dots cannot be shorter than ‘64’. For exapmle, neither ‘64.’ nor ‘16...’ will be accepted since both of the last dots indicate the half of ‘64’ (i.e. the duration of 1/128). In this problem, you are required to write a program that finds the shortest expressions equivalent to given sequences of rest commands. Input The input consists of multiple datasets. The first line of the input contains the number of datasets N . Then, N datasets follow, each containing a sequence of valid rest commands in one line. You may assume that no sequence contains more than 100,000 characters. Output For each dataset, your program should output the shortest expression in one line. If there are multiple expressions of the shortest length, output the lexicographically smallest one. Sample Input 3 R2R2 R1R2R4R8R16R32R64 R1R4R16 Output for the Sample Input R1 R1...... R16R1R4	36,106
Matrix Operation You are a student looking for a job. Today you had an employment examination for an IT company. They asked you to write an efficient program to perform several operations. First, they showed you an N \times N square matrix and a list of operations. All operations but one modify the matrix, and the last operation outputs the character in a specified cell. Please remember that you need to output the final matrix after you finish all the operations. Followings are the detail of the operations: WR r c v (Write operation) write a integer v into the cell (r,c) ( 1 \leq v \leq 1,000,000 ) CP r1 c1 r2 c2 (Copy operation) copy a character in the cell (r1,c1) into the cell (r2,c2) SR r1 r2 (Swap Row operation) swap the r1-th row and r2-th row SC c1 c2 (Swap Column operation) swap the c1-th column and c2-th column RL (Rotate Left operation) rotate the whole matrix in counter-clockwise direction by 90 degrees RR (Rotate Right operation) rotate the whole matrix in clockwise direction by 90 degrees RH (Reflect Horizontal operation) reverse the order of the rows RV (Reflect Vertical operation) reverse the order of the columns Input First line of each testcase contains nine integers. First two integers in the line, N and Q, indicate the size of matrix and the number of queries, respectively (1 \leq N,Q \leq 40,000) . Next three integers, A B, and C, are coefficients to calculate values in initial matrix (1 \leq A,B,C \leq 1,000,000) , and they are used as follows: A_{r,c} = (r * A + c * B) mod C where r and c are row and column indices, respectively (1\leq r,c\leq N) . Last four integers, D, E, F, and G, are coefficients to compute the final hash value mentioned in the next section (1 \leq D \leq E \leq N, 1 \leq F \leq G \leq N, E - D \leq 1,000, G - F \leq 1,000) . Each of next Q lines contains one operation in the format as described above. Output Output a hash value h computed from the final matrix B by using following pseudo source code. h <- 314159265 for r = D...E for c = F...G h <- (31 * h + B_{r,c}) mod 1,000,000,007 where "<-" is a destructive assignment operator, "for i = S...T" indicates a loop for i from S to T (both inclusive), and "mod" is a remainder operation. Sample Input 1 2 1 3 6 12 1 2 1 2 WR 1 1 1 Output for the Sample Input 1 676573821 Sample Input 2 2 1 3 6 12 1 2 1 2 RL Output for the Sample Input 2 676636559 Sample Input 3 2 1 3 6 12 1 2 1 2 RH Output for the Sample Input 3 676547189 Sample Input 4 39989 6 999983 999979 999961 1 1000 1 1000 SR 1 39989 SC 1 39989 RL RH RR RV Output for the Sample Input 4 458797120	36,107
Problem C: Changing Grids Background A君とB君は、『Changing Grids』というゲームに熱中している。このゲームは2人用で、プレイヤー1がステージを構成し、プレイヤー2がそのステージに挑戦しゴールを目指すというものである。今、A君とB君はこのゲームを何度かプレイしているが、A君の連勝でB君は1度も勝つことができていない。そこであなたは、B君にこのゲームを攻略するためのヒントを教えてあげることにした。 Problem 時刻 T 0 = 0における縦 H ×横 W の大きさの二次元グリッドの状態が Area 0 として与えられる。次に、このグリッドの状態は時刻 T i において、状態 Area i に切り替わる。この切り替わる過程は N 回繰り返される。初期状態のグリッドにはスタートの位置'S'とゴールの位置'G'が与えられる。いずれかのグリッドにおいてゴールへ辿り着ける場合は、そのときの最小歩数を出力し、ゴールへ辿り着けない場合は、'-1'を出力せよ。なお、以下の条件も満たす必要がある。 Area i は以下の要素で構成されている。 ‘.’は何もなく移動可能なマス ’#’は障害物であり、移動不可能なマス 'S'はスタート位置を表すマス 'G'はゴール位置を表すマスプレイヤーは現在いるマスの隣接している上下左右のいずれか1マスに移動する、または現在いるマスに留まるのに1秒かかる。ただし、障害物のマスやグリッドの範囲外には移動できない。歩数は、現在プレイヤーがいるマスから上下左右のマスへ1マス進むと1増加する。その場に留まる場合には増加しない。全てのグリッドの大きさは縦 H ×横 W である。 1マス移動、またはその場に留まった後にグリッドが切り替わる際、次のグリッドにおいて障害物が存在しないマスであれば今のグリッドの状態に関わらず移動が可能である。全てのグリッドにおいて、初期のグリッドに与えられたゴール位置に到達した場合ゴールとみなす。 Input 入力は以下の形式で与えられる。 H W Area 0 N T 1 Area 1 T 2 Area 2 . . T N Area N 1行目に2つの整数 H,W が空白区切りで与えられる。これは、それぞれ二次元グリッドの縦と横の大きさを表す。2行目から H +1行目までの各行に初期状態の二次元グリッドの状態が与えられる。 H +2行目に整数 N が与えられる。これは、二次元グリッドの変化する回数を表す。 H +3行目以降に N 個の二次元グリッドの切り替わる時刻 T i とその状態が与えられる。ただし、 T i は全て整数である。 Constraints 入力は以下の条件を満たす。 2 ≤ H,W ≤ 20 1 ≤ N ≤ 15 1 ≤ T i ≤ 200 ( T 1 < T 2 < ... < T N ) スタート位置'S'とゴール位置'G'はそれぞれ初期の二次元グリッドに1つだけ存在する。 Output スタートからゴールへ到達するための最小の歩数を出力せよ。ただし、ゴールに到達できない場合は'-1'を出力せよ。 Sample Input 1 2 2 S. .G 1 3 ## ## Sample Output 1 2 1番目のグリッドに切り替わる時刻 T 1 は3であり、時間内にプレイヤーはスタートからゴールまでの最短歩数が2歩で辿り着くことが可能なので2を出力する。 Sample Input 2 2 2 S. .G 1 2 ## ## Sample Output 2 -1 Sample Input 3 2 3 S## ##G 4 2 ### .## 3 ### #.# 5 ### ##. 7 ### ### Sample Output 3 3 Sample Input 4 4 3 S.. ... .G. ... 4 2 ### #.# ### #.# 4 ### #.. #.. ### 6 ### #.# ### #.. 8 ### #.. #.. ### Sample Output 4 3 Sample Input 5 3 3 S## ### ##G 1 1 ... ... ... Sample Output 5 4	36,108
気温の差選手の皆さん、パソコン甲子園にようこそ。イベントに参加するには体調管理が大切です。気温が大きく変動する季節の変わり目には体に負担がかかり、風邪をひきやすいと言われています。一番気を付けなければいけない日は、最高気温と最低気温の差が最も大きい日です。１日の最高気温と最低気温が７日分与えられたとき、それぞれの日について最高気温から最低気温を引いた値を出力するプログラムを作成してください。入力入力データは以下の形式で与えられる。 a 1 b 1 a 2 b 2 : a 7 b 7 入力は7行からなり、i行目には i 日目の最高気温 a i (-40 ≤ a i ≤ 40)と最低気温 b i (-40 ≤ b i ≤ 40)を表す整数が与えられる。すべての日において、最高気温 a i は必ず最低気温 b i 以上となっている。出力 7日分の気温の差を7行に出力する。入力例 30 19 39 20 19 18 25 20 22 21 23 10 10 -10 出力例 11 19 1 5 1 13 20	36,109
B: 山手線ゲーム - Yamanote-line Game - 豆（？）知識山手線は便利である。なぜならば、130円払うだけで時間の許す限り何周でも乗っていられるからだ。ただし、切符で乗車する場合は、切符の有効時間に気をつけなければならない。ICカードなら安心らしい。この山手線の特性を利用して、東京近郊には電車に揺られながら惰眠を貪る輩が存在する。ちなみに、この問題の作問者はやったことがない。駅員にバレることは稀だろうが、バレたらめんどくさそうなので、オススメはしない。問題文山手線の特性を利用したゲームをしよう。ここでは一般化のため、 1 から N で番号付けられた N 個の駅があり、 1 , 2 , ..., N の順で駅が円上に並び、各駅からいずれの駅へ行くにも d 円で乗車可能な路線として山手線モドキを考えることにする。ゲームは以下のルールに従う。好きな駅をスタート地点に選び d 円で山手線モドキに乗車する。その後、任意の駅で降車し再度乗車することを繰り返す。スタートした駅で降車した時点でゲーム終了となる。 i 番目の駅で降りると p_i 円の報酬を得ることができる．ただし、1度報酬を得た駅で再度報酬を得ることはできない。また、降車した後に再度山手線モドキに乗車するには d 円かかる。さて、あなたは最大で何円儲けることができるだろうか。ぜひ、挑戦してみて欲しい。入力形式 N d p_1 p_2 … p_N 入力はすべて整数からなる。 1行目には、山手線モドキの駅の数 N と乗車賃 d が空白区切りで与えられる。 2行目には、各駅でもらえる報酬が空白区切りで与えられ、 i 番目の値 p_i は駅 i の報酬を表している。制約 3 ≤ N ≤ 1{,}000 1 ≤ d ≤ 1{,}000 1 ≤ p_i ≤ 1{,}000 ( 1 ≤ i ≤ N ) 出力形式ゲームで得られる金額の最大値を1行に出力せよ。1円以上の金額を得ることができない場合は"kusoge"と1行に出力せよ。出力の最後は改行し余計な文字を含んではならない。入力例1 5 130 130 170 100 120 140 出力例1 50 入力例2 3 100 100 90 65 出力例2 kusoge 入力例3 6 210 300 270 400 330 250 370 出力例3 660 入力例4 4 540 100 460 320 280 出力例4 kusoge	36,110
Problem A: Sleeping Cats Jackは彼の住む家をとても気に入っていた. 彼の家の塀の上で毎日のように愛くるしいねこたちが昼寝をしているからだ. Jackはねこがとても好きだった. Jackは, 夏休みの自由研究としてねこたちの観察日記を付けることにした. しばらく観察しているうちに, 彼はねこたちの面白い特徴に気付いた. 塀は W[尺] の幅があり, ここにねこたちは並んで昼寝をする. それぞれのねこたちは体の大きさが違うので, 昼寝に必要とする幅もまた異なる. 昼寝をしにきたねこは, 自分が寝られる場所があれば, そこで昼寝をする. ただし, そのような場所が複数ある場合はより左側で昼寝をし, 十分な幅が無ければ諦めて帰ってしまう. しばらく昼寝をしたねこは、起きると塀から飛び降りてどこかへと行ってしまう. Jackはねこたちを観察して, その行動をノートに書き留めた. しかし, とても多くのねこが昼寝をしていたので, この記録を集計するのはとても大変である. プログラムを書いて, ねこたちが昼寝をした場所を求めるのを手伝ってほしい. Input 入力ファイルは, 複数のデータセットを含む. それぞれのデータセットの最初の行は2つの整数を含み, それぞれ塀の幅 W と, 後に続く行数 Q を表す. 以下のQ行に, ねこの観察記録が与えられる. 各行は, 以下のいずれかの書式に従う. s [id] [w] w [id] 前者は, ねこの sleep 記録であり, ねこが昼寝をしに来たことを表す. id はねこの名前を表す整数であり, w はそのねこが昼寝に必要とする幅 [尺]である. 後者は, ねこの wakeup 記録であり, 名前がidであるねこが起きたことを表す. この記録は, 時系列順に与えられる. どのねこも2回以上昼寝をすることはない. また, Jackの記録に矛盾は無いものとする. つまり, あるねこの sleep 記録に対して, そのねこが昼寝することが出来た場合, またその場合に限って, そのねこの wakeup 記録が(より後の行に)与えられる. W, Q ≤ 100 と仮定してよい. W と Q がともに 0 のとき、入力の終わりを示す. このデータセットに対する出力を行ってはならない. Output 入力のsleep記録が与えられるたびに, 1行出力せよ. この行は, もしそのねこが昼寝できた場合, その位置を表す数字を含まなければならない. ねこが塀の左端を起点として b [尺] から b+w [尺] の場所で昼寝したならば, b を出力せよ. そのねこが昼寝できなかった場合, " impossible " と出力せよ. データセットの終わりに, "END"と出力せよ. Sample Input 4 6 s 0 2 s 1 3 s 2 1 w 0 s 3 3 s 4 2 3 3 s 0 1 s 1 1 s 2 1 0 0 Output for the Sample Input 0 impossible 2 impossible 0 END 0 1 2 END	36,111
C: ツイート数問題 AORイカちゃんが利用するSNSであるイカったーでは、投稿のことをツイートと呼ぶ。そして、イカったーでは、ツイートへの返信が多くなると視認性が悪くなることが懸念されるため、あるツイートが次の規則のいずれかを満たすときに画面にそのツイートを表示する仕様になっている。規則１. どのツイートへも返信していない規則２. どのツイートからも返信されていない規則３. 規則２が適用されたツイートから返信先を順に辿ったとき、 $K$ 回未満で辿り着けるなお、同じツイートは重複して表示されることはない。いま、 $N$ 個のツイートがあり、 $A_i$ が $0$ のとき $i$ 番目のツイートは返信でないツイートで、 $A_i$ が $0$ でないとき $i$ 番目のツイートは $A_i$ 番目のツイートへの返信のツイートである。画面に表示されるツイート数を答えよ。制約 $1 \le N \le 10^5$ $1 \le K \le 10^5$ $0 \le A_i \lt i (i = 1, 2, \dots, N)$ ツイートは時系列順に与えられる。入力は全て整数で与えられる。入力形式入力は以下の形式で与えられる。 $N \ K$ $A_1$ $A_2$ $\vdots$ $A_N$ 出力画面に表示されるツイート数を出力せよ。また、末尾に改行も出力せよ。サンプルサンプル入力 1 6 3 0 0 2 3 4 5 サンプル出力 1 5 この時、表示されるツイートは、図の青いツイートである。よって、この例の解は $5$ である。サンプル入力 2 12 2 0 1 0 3 4 3 6 7 0 9 10 11 サンプル出力 2 10 サンプル入力 3 5 10 0 0 0 0 0 サンプル出力 3 5	36,112
Problem I: Explosion Problem 大魔王めぐみんは地上に生存する$N$人の勇者を倒そうと考えている。めぐみんは$M$回まで爆発魔法を唱えることができる。爆発魔法は任意の座標を中心に半径$r$以内に存在している勇者を消滅させる魔法である。勇者はとても痩せているため大きさは考慮しなくてよい。 $M$回の爆発魔法は全て同じ大きさの半径で唱えるものとする。勇者を全滅させるのに必要最小限の半径の魔法を使うことにした。爆発魔法の半径の大きさを最小化せよ。 Input $N$ $M$ $x_1$ $y_1$ ... $x_N$ $y_N$ 入力は以下の形式で与えられる。 1行目に勇者の数 $N$ 、唱える爆発の数 $M$ が整数で与えられる。 2行目以降にそれぞれの勇者$i$の座標 $x_i$ $,$ $y_i$ が整数で与えられる。 Constraints 入力は以下の条件を満たす。 $1 \leq M \leq N \leq 14$ $0 \leq x_i $,$ y_i \leq 10^5$ Output 爆発魔法の半径の最小値を実数で出力せよ。 $10^{-3}$を超える絶対誤差を含んではならない。 Sample Input 1 5 2 0 0 5 5 10 10 100 100 200 200 Sample Output 1 70.710678118755 Sample Input 2 10 5 321 675 4312 6534 312 532 412 6543 21 43 654 321 543 0 32 5 41 76 5 1 Sample Output 2 169.824909833728 Sample Input 3 14 3 312 342 4893 432 321 4 389 4 23 543 0 0 1 1 2 2 432 12 435 32 1 5 2 10 100 100 20 50 Sample Output 3 218.087711712613 Sample Input 4 5 2 0 0 0 0 0 0 0 0 0 0 Sample Output 4 0.000000000001	36,113
Problem A: The Mean of Angles Problem 与えられた2つの角度 θ 1 , θ 2 のちょうど間の角度を求めよ。ここで、ちょうど間の角度を、下図のように「 θ 1 + t = θ 2 − t を満たす t のうち絶対値が最も小さいものを t’ としたときの θ 1 + t’ 」と定義する。 Input 入力は以下の形式で与えられる。 θ 1 θ 2 Constraints 入力は以下の条件を満たす。角度は度数法(degree)で表される 0 ≤ θ 1 , θ 2 < 360 θ 1 , θ 2 は整数 \| θ 1 − θ 2 \| ≠ 180 解答が[0,0.0001]または[359.999, 360)になるような入力は与えられない Output θ 1 , θ 2 のちょうど間の角度を度数法で[0,360)の範囲で1行に出力せよ。ただし0.0001を超える誤差を含んではならない。 Sample Input 1 10 20 Sample Output 1 15.0 Sample Input 2 20 350 Sample Output 2 5.0	36,114
Score : 100 points Problem Statement You are given a grid of N rows and M columns. The square at the i -th row and j -th column will be denoted as (i,j) . A nonnegative integer A_{i,j} is written for each square (i,j) . You choose some of the squares so that each row and column contains at most K chosen squares. Under this constraint, calculate the maximum value of the sum of the integers written on the chosen squares. Additionally, calculate a way to choose squares that acheives the maximum. Constraints 1 \leq N \leq 50 1 \leq K \leq N 0 \leq A_{i,j} \leq 10^9 All values in Input are integer. Input Input is given from Standard Input in the following format: N K A_{1,1} A_{1,2} \cdots A_{1,N} A_{2,1} A_{2,2} \cdots A_{2,N} \vdots A_{N,1} A_{N,2} \cdots A_{N,N} Output On the first line, print the maximum value of the sum of the integers written on the chosen squares. On the next N lines, print a way that achieves the maximum. Precisely, output the strings t_1,t_2,\cdots,t_N , that satisfies t_{i,j}= X if you choose (i,j) and t_{i,j}= . otherwise. You may print any way to choose squares that maximizes the sum. Sample Input 1 3 1 5 3 2 1 4 8 7 6 9 Sample Output 1 19 X.. ..X .X. Sample Input 2 3 2 10 10 1 10 10 1 1 1 10 Sample Output 2 50 XX. XX. ..X	36,115
Score : 300 points Problem Statement Takahashi is organizing a party. At the party, each guest will receive one or more snack pieces. Takahashi predicts that the number of guests at this party will be A or B . Find the minimum number of pieces that can be evenly distributed to the guests in both of the cases predicted. We assume that a piece cannot be divided and distributed to multiple guests. Constraints 1 \leq A, B \leq 10^5 A \neq B All values in input are integers. Input Input is given from Standard Input in the following format: A B Output Print the minimum number of pieces that can be evenly distributed to the guests in both of the cases with A guests and B guests. Sample Input 1 2 3 Sample Output 1 6 When we have six snack pieces, each guest can take three pieces if we have two guests, and each guest can take two if we have three guests. Sample Input 2 123 456 Sample Output 2 18696 Sample Input 3 100000 99999 Sample Output 3 9999900000	36,116
Score : 300 points Problem Statement Takahashi, Aoki and Snuke love cookies. They have A , B and C cookies, respectively. Now, they will exchange those cookies by repeating the action below: Each person simultaneously divides his cookies in half and gives one half to each of the other two persons. This action will be repeated until there is a person with odd number of cookies in hand. How many times will they repeat this action? Note that the answer may not be finite. Constraints 1 ≤ A,B,C ≤ 10^9 Input Input is given from Standard Input in the following format: A B C Output Print the number of times the action will be performed by the three people, if this number is finite. If it is infinite, print -1 instead. Sample Input 1 4 12 20 Sample Output 1 3 Initially, Takahashi, Aoki and Snuke have 4 , 12 and 20 cookies. Then, After the first action, they have 16 , 12 and 8 . After the second action, they have 10 , 12 and 14 . After the third action, they have 13 , 12 and 11 . Now, Takahashi and Snuke have odd number of cookies, and therefore the answer is 3 . Sample Input 2 14 14 14 Sample Output 2 -1 Sample Input 3 454 414 444 Sample Output 3 1	36,117
Score : 700 points Problem Statement You are given four integers: H , W , h and w ( 1 ≤ h ≤ H , 1 ≤ w ≤ W ). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive: The matrix has H rows and W columns. Each element of the matrix is an integer between -10^9 and 10^9 (inclusive). The sum of all the elements of the matrix is positive. The sum of all the elements within every subrectangle with h rows and w columns in the matrix is negative. Constraints 1 ≤ h ≤ H ≤ 500 1 ≤ w ≤ W ≤ 500 Input Input is given from Standard Input in the following format: H W h w Output If there does not exist a matrix that satisfies all of the conditions, print No . Otherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format: a_{11} ... a_{1W} : a_{H1} ... a_{HW} Here, a_{ij} represents the (i,\ j) element of the matrix. Sample Input 1 3 3 2 2 Sample Output 1 Yes 1 1 1 1 -4 1 1 1 1 The sum of all the elements of this matrix is 4 , which is positive. Also, in this matrix, there are four subrectangles with 2 rows and 2 columns as shown below. For each of them, the sum of all the elements inside is -1 , which is negative. Sample Input 2 2 4 1 2 Sample Output 2 No Sample Input 3 3 4 2 3 Sample Output 3 Yes 2 -5 8 7 3 -5 -4 -5 2 1 -1 7	36,118
Score : 300 points Problem Statement "Pizza At", a fast food chain, offers three kinds of pizza: "A-pizza", "B-pizza" and "AB-pizza". A-pizza and B-pizza are completely different pizzas, and AB-pizza is one half of A-pizza and one half of B-pizza combined together. The prices of one A-pizza, B-pizza and AB-pizza are A yen, B yen and C yen (yen is the currency of Japan), respectively. Nakahashi needs to prepare X A-pizzas and Y B-pizzas for a party tonight. He can only obtain these pizzas by directly buying A-pizzas and B-pizzas, or buying two AB-pizzas and then rearrange them into one A-pizza and one B-pizza. At least how much money does he need for this? It is fine to have more pizzas than necessary by rearranging pizzas. Constraints 1 ≤ A, B, C ≤ 5000 1 ≤ X, Y ≤ 10^5 All values in input are integers. Input Input is given from Standard Input in the following format: A B C X Y Output Print the minimum amount of money required to prepare X A-pizzas and Y B-pizzas. Sample Input 1 1500 2000 1600 3 2 Sample Output 1 7900 It is optimal to buy four AB-pizzas and rearrange them into two A-pizzas and two B-pizzas, then buy additional one A-pizza. Sample Input 2 1500 2000 1900 3 2 Sample Output 2 8500 It is optimal to directly buy three A-pizzas and two B-pizzas. Sample Input 3 1500 2000 500 90000 100000 Sample Output 3 100000000 It is optimal to buy 200000 AB-pizzas and rearrange them into 100000 A-pizzas and 100000 B-pizzas. We will have 10000 more A-pizzas than necessary, but that is fine.	36,119
Score : 600 points Problem Statement Let us define the oddness of a permutation p = { p_1,\ p_2,\ ...,\ p_n } of { 1,\ 2,\ ...,\ n } as \sum_{i = 1}^n \|i - p_i\| . Find the number of permutations of { 1,\ 2,\ ...,\ n } of oddness k , modulo 10^9+7 . Constraints All values in input are integers. 1 \leq n \leq 50 0 \leq k \leq n^2 Input Input is given from Standard Input in the following format: n k Output Print the number of permutations of { 1,\ 2,\ ...,\ n } of oddness k , modulo 10^9+7 . Sample Input 1 3 2 Sample Output 1 2 There are six permutations of { 1,\ 2,\ 3 }. Among them, two have oddness of 2 : { 2,\ 1,\ 3 } and { 1,\ 3,\ 2 }. Sample Input 2 39 14 Sample Output 2 74764168	36,120
Problem D Hidden Anagrams An anagram is a word or a phrase that is formed by rearranging the letters of another. For instance, by rearranging the letters of "William Shakespeare," we can have its anagrams "I am a weakish speller," "I'll make a wise phrase," and so on. Note that when $A$ is an anagram of $B$, $B$ is an anagram of $A$. In the above examples, differences in letter cases are ignored, and word spaces and punctuation symbols are freely inserted and/or removed. These rules are common but not applied here; only exact matching of the letters is considered. For two strings $s_1$ and $s_2$ of letters, if a substring $s'_1$ of $s_1$ is an anagram of a substring $s'_2$ of $s_2$, we call $s'_1$ a hidden anagram of the two strings, $s_1$ and $s_2$. Of course, $s'_2$ is also a hidden anagram of them. Your task is to write a program that, for given two strings, computes the length of the longest hidden anagrams of them. Suppose, for instance, that "anagram" and "grandmother" are given. Their substrings "nagr" and "gran" are hidden anagrams since by moving letters you can have one from the other. They are the longest since any substrings of "grandmother" of lengths five or more must contain "d" or "o" that "anagram" does not. In this case, therefore, the length of the longest hidden anagrams is four. Note that a substring must be a sequence of letters occurring consecutively in the original string and so "nagrm" and "granm" are not hidden anagrams. Input The input consists of a single test case in two lines. $s_1$ $s_2$ $s_1$ and $s_2$ are strings consisting of lowercase letters (a through z) and their lengths are between 1 and 4000, inclusive. Output Output the length of the longest hidden anagrams of $s_1$ and $s_2$. If there are no hidden anagrams, print a zero. Sample Input 1 anagram grandmother Sample Output 1 4 Sample Input 2 williamshakespeare iamaweakishspeller Sample Output 2 18 Sample Input 3 aaaaaaaabbbbbbbb xxxxxabababxxxxxabab Sample Output 3 6 Sample Input 4 abababacdcdcd efefefghghghghgh Sample Output 4 0	36,121
Score : 400 points Problem Statement There are N squares in a row. The leftmost square contains the integer A , and the rightmost contains the integer B . The other squares are empty. Aohashi would like to fill the empty squares with integers so that the following condition is satisfied: For any two adjacent squares, the (absolute) difference of the two integers in those squares is between C and D (inclusive). As long as the condition is satisfied, it is allowed to use arbitrarily large or small integers to fill the squares. Determine whether it is possible to fill the squares under the condition. Constraints 3 \leq N \leq 500000 0 \leq A \leq 10^9 0 \leq B \leq 10^9 0 \leq C \leq D \leq 10^9 All input values are integers. Input Input is given from Standard Input in the following format: N A B C D Output Print YES if it is possible to fill the squares under the condition; print NO otherwise. Sample Input 1 5 1 5 2 4 Sample Output 1 YES For example, fill the squares with the following integers: 1 , -1 , 3 , 7 , 5 , from left to right. Sample Input 2 4 7 6 4 5 Sample Output 2 NO Sample Input 3 48792 105960835 681218449 90629745 90632170 Sample Output 3 NO Sample Input 4 491995 412925347 825318103 59999126 59999339 Sample Output 4 YES	36,122
Score : 1000 points Problem Statement Problem F and F2 are the same problem, but with different constraints and time limits. We have a board divided into N horizontal rows and N vertical columns of square cells. The cell at the i -th row from the top and the j -th column from the left is called Cell (i,j) . Each cell is either empty or occupied by an obstacle. Also, each empty cell has a digit written on it. If A_{i,j}= 1 , 2 , ..., or 9 , Cell (i,j) is empty and the digit A_{i,j} is written on it. If A_{i,j}= # , Cell (i,j) is occupied by an obstacle. Cell Y is reachable from cell X when the following conditions are all met: Cells X and Y are different. Cells X and Y are both empty. One can reach from Cell X to Cell Y by repeatedly moving right or down to an adjacent empty cell. Consider all pairs of cells (X,Y) such that cell Y is reachable from cell X . Find the sum of the products of the digits written on cell X and cell Y for all of those pairs. Constraints 1 \leq N \leq 500 A_{i,j} is one of the following characters: 1 , 2 , ... 9 and # . Input Input is given from Standard Input in the following format: N A_{1,1}A_{1,2}...A_{1,N} A_{2,1}A_{2,2}...A_{2,N} : A_{N,1}A_{N,2}...A_{N,N} Output Print the sum of the products of the digits written on cell X and cell Y for all pairs (X,Y) such that cell Y is reachable from cell X . Sample Input 1 2 11 11 Sample Output 1 5 There are five pairs of cells (X,Y) such that cell Y is reachable from cell X , as follows: X=(1,1) , Y=(1,2) X=(1,1) , Y=(2,1) X=(1,1) , Y=(2,2) X=(1,2) , Y=(2,2) X=(2,1) , Y=(2,2) The product of the digits written on cell X and cell Y is 1 for all of those pairs, so the answer is 5 . Sample Input 2 4 1111 11#1 1#11 1111 Sample Output 2 47 Sample Input 3 10 76##63##3# 8445669721 75#9542133 3#285##445 749632##89 2458##9515 5952578#77 1#3#44196# 4355#99#1# #298#63587 Sample Output 3 36065 Sample Input 4 10 4177143673 7######### 5#1716155# 6#4#####5# 2#3#597#6# 6#9#8#3#5# 5#2#899#9# 1#6#####6# 6#5359657# 5######### Sample Output 4 6525	36,123
Score : 1400 points Problem Statement We have a grid with H rows and W columns. The state of the cell at the i -th ( 1≤i≤H ) row and j -th ( 1≤j≤W ) column is represented by a letter a_{ij} , as follows: . : This cell is empty. o : This cell contains a robot. E : This cell contains the exit. E occurs exactly once in the whole grid. Snuke is trying to salvage as many robots as possible, by performing the following operation some number of times: Select one of the following directions: up, down, left, right. All remaining robots will move one cell in the selected direction, except when a robot would step outside the grid, in which case the robot will explode and immediately disappear from the grid. If a robot moves to the cell that contains the exit, the robot will be salvaged and immediately removed from the grid. Find the maximum number of robots that can be salvaged. Constraints 2≤H,W≤100 a_{ij} is . , o or E . E occurs exactly once in the whole grid. Input The input is given from Standard Input in the following format: H W a_{11} ... a_{1W} : a_{H1} ... a_{HW} Output Print the maximum number of robots that can be salvaged. Sample Input 1 3 3 o.o .Eo ooo Sample Output 1 3 For example, select left, up, right. Sample Input 2 2 2 E. .. Sample Output 2 0 Sample Input 3 3 4 o... o... oooE Sample Output 3 5 Select right, right, right, down, down. Sample Input 4 5 11 ooo.ooo.ooo o.o.o...o.. ooo.oE..o.. o.o.o.o.o.. o.o.ooo.ooo Sample Output 4 12	36,124
Problem Statement JAG land is a country, which is represented as an $M \times M$ grid. Its top-left cell is $(1, 1)$ and its bottom-right cell is $(M, M)$. Suddenly, a bomber invaded JAG land and dropped bombs to the country. Its bombing pattern is always fixed and represented by an $N \times N$ grid. Each symbol in the bombing pattern is either X or . . The meaning of each symbol is as follows. X : Bomb . : Empty Here, suppose that a bomber is in $(br, bc)$ in the land and drops a bomb. The cell $(br + i - 1, bc + j - 1)$ will be damaged if the symbol in the $i$-th row and the $j$-th column of the bombing pattern is X ($1 \le i, j \le N$). Initially, the bomber reached $(1, 1)$ in JAG land. The bomber repeated to move to either of $4$-directions and then dropped a bomb just $L$ times. During this attack, the values of the coordinates of the bomber were between $1$ and $M - N + 1$, inclusive, while it dropped bombs. Finally, the bomber left the country. The moving pattern of the bomber is described as $L$ characters. The $i$-th character corresponds to the $i$-th move and the meaning of each character is as follows. U : Up D : Down L : Left R : Right Your task is to write a program to analyze the damage situation in JAG land. To investigate damage overview in the land, calculate the number of cells which were damaged by the bomber at least $K$ times. Input The input consists of a single test case in the format below. $N$ $M$ $K$ $L$ $B_{1}$ $\vdots$ $B_{N}$ $S$ The first line contains four integers $N$, $M$, $K$ and $L$($1 \le N < M \le 500$, $1 \le K \le L \le 2 \times 10^{5}$). The following $N$ lines represent the bombing pattern. $B_i$ is a string of length $N$. Each character of $B_i$ is either X or . . The last line denotes the moving pattern. $S$ is a string of length $L$, which consists of either U , D , L or R . It's guaranteed that the values of the coordinates of the bomber are between $1$ and $M - N + 1$, inclusive, while it drops bombs in the country. Output Print the number of cells which were damaged by the bomber at least $K$ times. Examples Input Output 2 3 2 4 XX X. RDLU 3 7 8 3 5 .XXX.X. X..X.X. ...XX.X XX.XXXX ..XXXX. X.X.... ..XXXXX DRULD 26	36,125
Enumeration of Subsets I Print all subsets of a set $S$, which contains $0, 1, ... n-1$ as elements. Note that we represent $0, 1, ... n-1$ as 00...0001, 00...0010, 00...0100, ..., 10...0000 in binary respectively and the integer representation of a subset is calculated by bitwise OR of existing elements. Input The input is given in the following format. $n$ Output Print subsets ordered by their decimal integers. Print a subset in a line in the following format. $d$: $e_0$ $e_1$ ... Print ' : ' after the integer value $d$, then print elements $e_i$ in the subset in ascending order. Seprate two adjacency elements by a space character. Constraints $1 \leq n \leq 18$ Sample Input 1 4 Sample Output 1 0: 1: 0 2: 1 3: 0 1 4: 2 5: 0 2 6: 1 2 7: 0 1 2 8: 3 9: 0 3 10: 1 3 11: 0 1 3 12: 2 3 13: 0 2 3 14: 1 2 3 15: 0 1 2 3 Note that if the subset is empty, your program should not output a space character after ' : '.	36,126
Flipping Colors You are given an undirected complete graph. Every pair of the nodes in the graph is connected by an edge, colored either red or black. Each edge is associated with an integer value called penalty. By repeating certain operations on the given graph, a “spanning tree” should be formed with only the red edges. That is, the number of red edges should be made exactly one less than the number of nodes, and all the nodes should be made connected only via red edges, directly or indirectly. If two or more such trees can be formed, one with the least sum of penalties of red edges should be chosen. In a single operation step, you choose one of the nodes and flip the colors of all the edges connected to it: Red ones will turn to black, and black ones to red. Fig. F-1 The first dataset of Sample Input and its solution For example, the leftmost graph of Fig. F-1 illustrates the first dataset of Sample Input. By flipping the colors of all the edges connected to the node 3, and then flipping all the edges connected to the node 2, you can form a spanning tree made of red edges as shown in the rightmost graph of the figure. Input The input consists of multiple datasets, each in the following format. n e 1,2 e 1,3 ... e 1, n -1 e 1, n e 2,3 e 2,4 ... e 2, n ... e n -1, n The integer n (2 ≤ n ≤ 300) is the number of nodes. The nodes are numbered from 1 to n . The integer e i , k (1 ≤ \| e i , k \| ≤ 10 5 ) denotes the penalty and the initial color of the edge between the node i and the node k . Its absolute value \| e i , k \| represents the penalty of the edge. e i , k > 0 means that the edge is initially red, and e i , k < 0 means it is black. The end of the input is indicated by a line containing a zero. The number of datasets does not exceed 50. Output For each dataset, print the sum of edge penalties of the red spanning tree with the least sum of edge penalties obtained by the above-described operations. If a red spanning tree can never be made by such operations, print -1 . Sample Input 4 3 3 1 2 6 -4 3 1 -10 100 5 -2 -2 -2 -2 -1 -1 -1 -1 -1 1 4 -4 7 6 2 3 -1 0 Output for the Sample Input 7 11 -1 9	36,127
Problem B: Artistic Art Museum Mr. Knight is a chief architect of the project to build a new art museum. One day, he was struggling to determine the design of the building. He believed that a brilliant art museum must have an artistic building, so he started to search for a good motif of his building. The art museum has one big theme: "nature and human beings." To reflect the theme, he decided to adopt a combination of a cylinder and a prism, which symbolize nature and human beings respectively (between these figures and the theme, there is a profound relationship that only he knows). Shortly after his decision, he remembered that he has to tell an estimate of the cost required to build to the financial manager. He unwillingly calculated it, and he returned home after he finished his report. However, you, an able secretary of Mr. Knight, have found that one field is missing in his report: the length of the fence required to surround the building. Fortunately you are also a good programmer, so you have decided to write a program that calculates the length of the fence. To be specific, the form of his building is union of a cylinder and a prism. You may consider the twodimensional projection of the form, i.e. the shape of the building is considered to be union of a circle C and a polygon P . The fence surrounds the outside of the building. The shape of the building may have a hole in it, and the fence is not needed inside the building. An example is shown in the figure below. Input The input contains one test case. A test case has the following format: R N x 1 y 1 x 2 y 2 ... x n y n R is an integer that indicates the radius of C (1 ≤ R ≤ 1000), whose center is located at the origin. N is the number of vertices of P , and ( x i , y i ) is the coordinate of the i -th vertex of P . N , x i and y i are all integers satisfying the following conditions: 3 ≤ N ≤ 100,\| x i \| ≤ 1000 and \| y i \| ≤ 1000. You may assume that C and P have one or more intersections. Output Print the length of the fence required to surround the building. The output value should be in a decimal fraction may not contain an absolute error more than 10 -4 . It is guaranteed that the answer does not change by more than 10 -6 when R is changed by up to 10 -9 . Sample Input 1 2 8 -1 2 1 2 1 -3 2 -3 2 3 -2 3 -2 -3 -1 -3 Output for the Sample Input 1 22.6303	36,128
500-yen Saving "500-yen Saving" is one of Japanese famous methods to save money. The method is quite simple; whenever you receive a 500-yen coin in your change of shopping, put the coin to your 500-yen saving box. Typically, you will find more than one million yen in your saving box in ten years. Some Japanese people are addicted to the 500-yen saving. They try their best to collect 500-yen coins efficiently by using 1000-yen bills and some coins effectively in their purchasing. For example, you will give 1320 yen (one 1000-yen bill, three 100-yen coins and two 10-yen coins) to pay 817 yen, to receive one 500-yen coin (and three 1-yen coins) in the change. A friend of yours is one of these 500-yen saving addicts. He is planning a sightseeing trip and wants to visit a number of souvenir shops along his way. He will visit souvenir shops one by one according to the trip plan. Every souvenir shop sells only one kind of souvenir goods, and he has the complete list of their prices. He wants to collect as many 500-yen coins as possible through buying at most one souvenir from a shop. On his departure, he will start with sufficiently many 1000-yen bills and no coins at all. The order of shops to visit cannot be changed. As far as he can collect the same number of 500-yen coins, he wants to cut his expenses as much as possible. Let's say that he is visiting shops with their souvenir prices of 800 yen, 700 yen, 1600 yen, and 600 yen, in this order. He can collect at most two 500-yen coins spending 2900 yen, the least expenses to collect two 500-yen coins, in this case. After skipping the first shop, the way of spending 700-yen at the second shop is by handing over a 1000-yen bill and receiving three 100-yen coins. In the next shop, handing over one of these 100-yen coins and two 1000-yen bills for buying a 1600-yen souvenir will make him receive one 500-yen coin. In almost the same way, he can obtain another 500-yen coin at the last shop. He can also collect two 500-yen coins buying at the first shop, but his total expenditure will be at least 3000 yen because he needs to buy both the 1600-yen and 600-yen souvenirs in this case. You are asked to make a program to help his collecting 500-yen coins during the trip. Receiving souvenirs' prices listed in the order of visiting the shops, your program is to find the maximum number of 500-yen coins that he can collect during his trip, and the minimum expenses needed for that number of 500-yen coins. For shopping, he can use an arbitrary number of 1-yen, 5-yen, 10-yen, 50-yen, and 100-yen coins he has, and arbitrarily many 1000-yen bills. The shop always returns the exact change, i.e., the difference between the amount he hands over and the price of the souvenir. The shop has sufficient stock of coins and the change is always composed of the smallest possible number of 1-yen, 5-yen, 10-yen, 50-yen, 100-yen, and 500-yen coins and 1000-yen bills. He may use more money than the price of the souvenir, even if he can put the exact money, to obtain desired coins as change; buying a souvenir of 1000 yen, he can hand over one 1000-yen bill and five 100-yen coins and receive a 500-yen coin. Note that using too many coins does no good; handing over ten 100-yen coins and a 1000-yen bill for a souvenir of 1000 yen, he will receive a 1000-yen bill as the change, not two 500-yen coins. Input The input consists of at most 50 datasets, each in the following format. n p 1 ... p n n is the number of souvenir shops, which is a positive integer not greater than 100. p i is the price of the souvenir of the i -th souvenir shop. p i is a positive integer not greater than 5000. The end of the input is indicated by a line with a single zero. Output For each dataset, print a line containing two integers c and s separated by a space. Here, c is the maximum number of 500-yen coins that he can get during his trip, and s is the minimum expenses that he need to pay to get c 500-yen coins. Sample Input 4 800 700 1600 600 4 300 700 1600 600 4 300 700 1600 650 3 1000 2000 500 3 250 250 1000 4 1251 667 876 299 0 Output for the Sample Input 2 2900 3 2500 3 3250 1 500 3 1500 3 2217	36,129
Problem F: Dr. Podboq or: How We Became Asymmetric After long studying how embryos of organisms become asymmetric during their development, Dr. Podboq, a famous biologist, has reached his new hypothesis. Dr. Podboq is now preparing a poster for the coming academic conference, which shows a tree representing the development process of an embryo through repeated cell divisions starting from one cell. Your job is to write a program that transforms given trees into forms satisfying some conditions so that it is easier for the audience to get the idea. A tree representing the process of cell divisions has a form described below. The starting cell is represented by a circle placed at the top. Each cell either terminates the division activity or divides into two cells. Therefore, from each circle representing a cell, there are either no branch downward, or two branches down to its two child cells. Below is an example of such a tree. Figure F-1: A tree representing a process of cell divisions According to Dr. Podboq's hypothesis, we can determine which cells have stronger or weaker asymmetricity by looking at the structure of this tree representation. First, his hypothesis defines "left-right similarity" of cells as follows: The left-right similarity of a cell that did not divide further is 0. For a cell that did divide further, we collect the partial trees starting from its child or descendant cells, and count how many kinds of structures they have. Then, the left-right similarity of the cell is defined to be the ratio of the number of structures that appear both in the right child side and the left child side. We regard two trees have the same structure if we can make them have exactly the same shape by interchanging two child cells of arbitrary cells. For example, suppose we have a tree shown below: Figure F-2: An example tree The left-right similarity of the cell A is computed as follows. First, within the descendants of the cell B, which is the left child cell of A, the following three kinds of structures appear. Notice that the rightmost structure appears three times, but when we count the number of structures, we count it only once. Figure F-3: Structures appearing within the descendants of the cell B On the other hand, within the descendants of the cell C, which is the right child cell of A, the following four kinds of structures appear. Figure F-4: Structures appearing within the descendants of the cell C Among them, the first, second, and third ones within the B side are regarded as the same structure as the second, third, and fourth ones within the C side, respectively. Therefore, there are four structures in total, and three among them are common to the left side and the right side, which means the left-right similarity of A is 3/4. Given the left-right similarity of each cell, Dr. Podboq's hypothesis says we can determine which of the cells X and Y has stronger asymmetricity by the following rules. If X and Y have different left-right similarities, the one with lower left-right similarity has stronger asymmetricity. Otherwise, if neither X nor Y has child cells, they have completely equal asymmetricity. Otherwise, both X and Y must have two child cells. In this case, we compare the child cell of X with stronger (or equal) asymmetricity (than the other child cell of X ) and the child cell of Y with stronger (or equal) asymmetricity (than the other child cell of Y ), and the one having a child with stronger asymmetricity has stronger asymmetricity. If we still have a tie, we compare the other child cells of X and Y with weaker (or equal) asymmetricity, and the one having a child with stronger asymmetricity has stronger asymmetricity. If we still have a tie again, X and Y have completely equal asymmetricity. When we compare child cells in some rules above, we recursively apply this rule set. Now, your job is to write a program that transforms a given tree representing a process of cell divisions, by interchanging two child cells of arbitrary cells, into a tree where the following conditions are satisfied. For every cell X which is the starting cell of the given tree or a left child cell of some parent cell, if X has two child cells, the one at left has stronger (or equal) asymmetricity than the one at right. For every cell X which is a right child cell of some parent cell, if X has two child cells, the one at right has stronger (or equal) asymmetricity than the one at left. In case two child cells have equal asymmetricity, their order is arbitrary because either order would results in trees of the same shape. For example, suppose we are given the tree in Figure F-2. First we compare B and C, and because B has lower left-right similarity, which means stronger asymmetricity, we keep B at left and C at right. Next, because B is the left child cell of A, we compare two child cells of B, and the one with stronger asymmetricity is positioned at left. On the other hand, because C is the right child cell of A, we compare two child cells of C, and the one with stronger asymmetricity is positioned at right. We examine the other cells in the same way, and the tree is finally transformed into the tree shown below. Figure F-5: The example tree after the transformation Please be warned that the only operation allowed in the transformation of a tree is to interchange two child cells of some parent cell. For example, you are not allowed to transform the tree in Figure F-2 into the tree below. Figure F-6: An example of disallowed transformation Input The input consists of n lines (1≤ n ≤100) describing n trees followed by a line only containing a single zero which represents the end of the input. Each tree includes at least 1 and at most 127 cells. Below is an example of a tree description. ((x (x x)) x) This description represents the tree shown in Figure F-1. More formally, the description of a tree is in either of the following two formats. " ( " <description of a tree starting at the left child> <single space> <description of a tree starting at the right child> ")" or " x " The former is the description of a tree whose starting cell has two child cells, and the latter is the description of a tree whose starting cell has no child cell. Output For each tree given in the input, print a line describing the result of the tree transformation. In the output, trees should be described in the same formats as the input, and the tree descriptions must appear in the same order as the input. Each line should have no extra character other than one tree description. Sample Input (((x x) x) ((x x) (x (x x)))) (((x x) (x x)) ((x x) ((x x) (x x)))) (((x x) ((x x) x)) (((x (x x)) x) (x x))) (((x x) x) ((x x) (((((x x) x) x) x) x))) (((x x) x) ((x (x x)) (x (x x)))) ((((x (x x)) x) (x ((x x) x))) ((x (x x)) (x x))) ((((x x) x) ((x x) (x (x x)))) (((x x) (x x)) ((x x) ((x x) (x x))))) 0 Output for the Sample Input ((x (x x)) ((x x) ((x x) x))) (((x x) ((x x) (x x))) ((x x) (x x))) (((x ((x x) x)) (x x)) ((x x) ((x x) x))) (((x ((x ((x x) x)) x)) (x x)) ((x x) x)) ((x (x x)) ((x (x x)) ((x x) x))) (((x (x x)) (x x)) ((x ((x x) x)) ((x (x x)) x))) (((x (x x)) ((x x) ((x x) x))) (((x x) (x x)) (((x x) (x x)) (x x))))	36,130
Problem D: Identity Function You are given an integer $N$, which is greater than 1. Consider the following functions: $f(a) = a^N$ mod $N$ $F_1(a) = f(a)$ $F_{k+1}(a) = F_k(f(a))$ $(k = 1,2,3,...)$ Note that we use mod to represent the integer modulo operation. For a non-negative integer $x$ and a positive integer $y$, $x$ mod $y$ is the remainder of $x$ divided by $y$. Output the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than $N$. If no such $k$ exists, output -1. Input The input consists of a single line that contains an integer $N$ ($2 \leq N \leq 10^9$), whose meaning is described in the problem statement. Output Output the minimum positive integer $k$ such that $F_k(a) = a$ for all positive integers $a$ less than $N$, or -1 if no such $k$ exists. Sample Input 3 Output for the Sample Input 1 Sample Input 4 Output for the Sample Input -1 Sample Input 15 Output for the Sample Input 2	36,131
Flag AHK Education, the educational program section of Aizu Broadcasting Cooperation, broadcasts a children’s workshop program called "Let's Play and Make." Today’s theme is "Make your own flag." A child writes his first initial in the center of their rectangular flag. Given the flag size and the initial letter to be placed in the center of it, write a program to draw the flag as shown in the figure below. +-------+ \|.......\| \|...A...\| \|.......\| +-------+ The figure has "A" in the center of a flag with size 9 (horizontal) × 5 (vertical). Input The input is given in the following format. W H c The input line provides the flag dimensions W (width) and H (height) (3 ≤ W,H ≤ 21), and the initial letter c . Both W and H are odd numbers, and c is a capital letter. Output Draw the flag of specified size with the initial in its center using the following characters: " + " for the four corners of the flag, " - " for horizontal lines, " \| " for vertical lines, and " . " for the background (except for the initial in the center). Sample Input 1 3 3 B Sample Output 1 +-+ \|B\| +-+ Sample Input 2 11 7 Z Sample Output 2 +---------+ \|.........\| \|.........\| \|....Z....\| \|.........\| \|.........\| +---------+	36,132
Nets of Dice In mathematics, some plain words have special meanings. The word " net " is one of such technical terms. In mathematics, the word " net " is sometimes used to mean a plane shape which can be folded into some solid shape. The following are a solid shape (Figure 1) and one of its net (Figure 2). Figure 1: a prism Figure 2: a net of a prism Nets corresponding to a solid shape are not unique. For example, Figure 3 shows three of the nets of a cube. Figure 3: examples of nets of a cube In this problem, we consider nets of dice. The definition of a die is as follows. A die is a cube, each face marked with a number between one and six. Numbers on faces of a die are different from each other. The sum of two numbers on the opposite faces is always 7. Usually, a die is used in pair with another die. The plural form of the word "die" is "dice". Some examples of proper nets of dice are shown in Figure 4, and those of improper ones are shown in Figure 5. Figure 4: examples of proper nets of dice Figure 5: examples of improper nets The reasons why each example in Figure 5 is improper are as follows. (a) The sum of two numbers on the opposite faces is not always 7. (b) Some faces are marked with the same number. (c) This is not a net of a cube. Some faces overlap each other. (d) This is not a net of a cube. Some faces overlap each other and one face of a cube is not covered. (e) This is not a net of a cube. The plane shape is cut off into two parts. The face marked with '2' is isolated. (f) This is not a net of a cube. The plane shape is cut off into two parts. (g) There is an extra face marked with '5'. Notice that there are two kinds of dice. For example, the solid shapes formed from the first two examples in Figure 4 are mirror images of each other. Any net of a die can be expressed on a sheet of 5x5 mesh like the one in Figure 6. In the figure, gray squares are the parts to be cut off. When we represent the sheet of mesh by numbers as in Figure 7, squares cut off are marked with zeros. Figure 6: 5x5 mesh Figure 7: representation by numbers Your job is to write a program which tells the proper nets of a die from the improper ones automatically. Input The input consists of multiple sheets of 5x5 mesh. N Mesh 0 Mesh 1 ... Mesh N -1 N is the number of sheets of mesh. Each Mesh i gives a sheet of mesh on which a net of a die is expressed. Mesh i is in the following format. F 00 F 01 F 02 F 03 F 04 F 10 F 11 F 12 F 13 F 14 F 20 F 21 F 22 F 23 F 24 F 30 F 31 F 32 F 33 F 34 F 40 F 41 F 42 F 43 F 44 Each F ij is an integer between 0 and 6. They are separated by a space character. Output For each Mesh i , the truth value, true or false , should be output, each in a separate line. When the net of a die expressed on the Mesh i is proper, output "true". Otherwise, output "false". Sample Input 6 0 0 0 0 0 0 0 0 0 6 0 2 4 5 3 0 0 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 2 0 0 0 0 4 1 0 0 0 0 5 0 0 0 0 6 0 0 0 0 3 0 0 0 2 5 0 0 4 1 0 0 0 0 6 0 0 0 0 0 0 0 0 6 2 0 0 0 0 4 0 0 0 1 5 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 6 0 2 4 5 3 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 0 2 4 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 Output for the Sample Input true true false false false false	36,133
KND is So Sexy Problem KND君は会津大学に在籍する学生プログラマである。彼の胸元はとてもセクシーなことで知られている。簡単のために胸元から見える肌の部分を図にある二等辺三角形ABCで表す。しかし服にはたるみが生じているため、長さが等しい2辺AC,BC(これらの長さを l とする)には実際にはさらに長さ x 分余裕がある。はだける部分の面積を増やすため、たるんだ分を引っ張ることで新たにふたつの三角形ADC,BECを作ることにしよう。点D,Eは三角形ABCの外側に存在する。この新しいふたつの三角形はたるみによって生じるもので、辺BEと辺ECの長さの和および辺ADと辺DCの長さの和は l + x でなければならない。あなたはこれら3つの三角形の面積の和 M が最大になるように点D,Eを決める。KND君の隣人であるあなたは彼の胸元がどれ程セクシーなのかを調べるために、 a , l , x を入力として服からのぞく肌の最大の面積( M )を計算するプログラムを作成することにした。 Input 入力は複数のテストケースからなる。ひとつのテストケースは以下の形式で与えられる。入力の終わりをEOFで示す。 a l x ここで、 a :三角形ABCの辺ABの長さ l :三角形ABCの2辺AC,BCの長さ x :2辺AC,BCにあるたるみである。 Constraints 入力は以下の条件を満たす。入力はすべて整数。 1 ≤ a ≤ 1000 1 ≤ l ≤ 1000 1 ≤ x ≤ 1000 Output 各テストケースにつき最大の面積を1行に出力せよ。この値はジャッジ出力の値と10 -5 より大きい差を持ってはならない。 Sample Input 2 2 1 2 3 1 3 2 3 2 3 5 Sample Output 3.9681187851 6.7970540913 6.5668891783 13.9527248554	36,134
Score : 400 points Problem Statement Mountaineers Mr. Takahashi and Mr. Aoki recently trekked across a certain famous mountain range. The mountain range consists of N mountains, extending from west to east in a straight line as Mt. 1 , Mt. 2 , ..., Mt. N . Mr. Takahashi traversed the range from the west and Mr. Aoki from the east. The height of Mt. i is h_i , but they have forgotten the value of each h_i . Instead, for each i ( 1 ≤ i ≤ N ), they recorded the maximum height of the mountains climbed up to the time they reached the peak of Mt. i (including Mt. i ). Mr. Takahashi's record is T_i and Mr. Aoki's record is A_i . We know that the height of each mountain h_i is a positive integer. Compute the number of the possible sequences of the mountains' heights, modulo 10^9 + 7 . Note that the records may be incorrect and thus there may be no possible sequence of the mountains' heights. In such a case, output 0 . Constraints 1 ≤ N ≤ 10^5 1 ≤ T_i ≤ 10^9 1 ≤ A_i ≤ 10^9 T_i ≤ T_{i+1} ( 1 ≤ i ≤ N - 1 ) A_i ≥ A_{i+1} ( 1 ≤ i ≤ N - 1 ) Input The input is given from Standard Input in the following format: N T_1 T_2 ... T_N A_1 A_2 ... A_N Output Print the number of possible sequences of the mountains' heights, modulo 10^9 + 7 . Sample Input 1 5 1 3 3 3 3 3 3 2 2 2 Sample Output 1 4 The possible sequences of the mountains' heights are: 1, 3, 2, 2, 2 1, 3, 2, 1, 2 1, 3, 1, 2, 2 1, 3, 1, 1, 2 for a total of four sequences. Sample Input 2 5 1 1 1 2 2 3 2 1 1 1 Sample Output 2 0 The records are contradictory, since Mr. Takahashi recorded 2 as the highest peak after climbing all the mountains but Mr. Aoki recorded 3 . Sample Input 3 10 1 3776 3776 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 8848 3776 5 Sample Output 3 884111967 Don't forget to compute the number modulo 10^9 + 7 . Sample Input 4 1 17 17 Sample Output 4 1 Some mountain ranges consist of only one mountain.	36,135
Revenge of the Endless BFS Mr. Endo wanted to write the code that performs breadth-first search (BFS), which is a search algorithm to explore all vertices on a directed graph. An example of pseudo code of BFS is as follows: 1: $current \leftarrow \{start\_vertex\}$ 2: $visited \leftarrow current$ 3: while $visited \ne$ the set of all the vertices 4: $found \leftarrow \{\}$ 5: for $u$ in $current$ 6: for each $v$ such that there is an edge from $u$ to $v$ 7: $found \leftarrow found \cup \{v\}$ 8: $current \leftarrow found \setminus visited$ 9: $visited \leftarrow visited \cup found$ However, Mr. Endo apparently forgot to manage visited vertices in his code. More precisely, he wrote the following code: 1: $current \leftarrow \{start\_vertex\}$ 2: while $current \ne$ the set of all the vertices 3: $found \leftarrow \{\}$ 4: for $u$ in $current$ 5: for each $v$ such that there is an edge from $u$ to $v$ 6: $found \leftarrow found \cup \{v\}$ 7: $current \leftarrow found$ You may notice that for some graphs, Mr. Endo's program will not stop because it keeps running infinitely. Notice that it does not necessarily mean the program cannot explore all the vertices within finite steps. Your task here is to make a program that determines whether Mr. Endo's program will stop within finite steps for a given directed graph in order to point out the bug to him. Also, calculate the minimum number of loop iterations required for the program to stop if it is finite. Since the answer might be huge, thus print the answer modulo $10^9 +7$, which is a prime number. Input The input consists of a single test case formatted as follows. $N$ $M$ $u_1$ $v_1$ : $u_M$ $v_M$ The first line consists of two integers $N$ ($2 \leq N \leq 500$) and $M$ ($1 \leq M \leq 200,000$), where $N$ is the number of vertices and $M$ is the number of edges in a given directed graph, respectively. The $i$-th line of the following $M$ lines consists of two integers $u_i$ and $v_i$ ($1 \leq u_i, v_i \leq N$), which means there is an edge from $u_i$ to $v_i$ in the given graph. The vertex $1$ is the start vertex, i.e. $start\_vertex$ in the pseudo codes. You can assume that the given graph also meets the following conditions. The graph has no self-loop, i.e., $u_i \ne v_i$ for all $1 \leq i \leq M$. The graph has no multi-edge, i.e., $(u_i, v_i) \le (u_j, v_j)$ for all $1 \leq i < j \leq M$. For each vertex $v$, there is at least one path from the start vertex $1$ to $v$. Output If Mr. Endo's wrong BFS code cannot stop within finite steps for the given input directed graph, print '-1' in a line. Otherwise, print the minimum number of loop iterations required to stop modulo $10^9+7$. Sample Input 1 4 4 1 2 2 3 3 4 4 1 Output for Sample Input 1 -1 Sample Input 2 4 5 1 2 2 3 3 4 4 1 1 3 Output for Sample Input 2 7 Sample Input 3 5 13 4 2 2 4 1 2 5 4 5 1 2 1 5 3 4 3 1 5 4 5 2 3 5 2 1 3 Output for Sample Input 3 3	36,136
ヒットアンドブロー太郎君と花子さんはヒットアンドブローで遊ぶことにしました。ヒットアンドブローのルールは、以下の通りです。出題者と回答者に分かれて行う。出題者は、重複した数を含まない 4 桁の数字(正解)を決める。回答者は、その 4 桁の数字(回答)を言い当てる。回答に対して、出題者はヒットとブローの数でヒントを与える。回答と正解を比べて、数と桁位置の両方が同じであることをヒットと呼び、数だけが同じで桁位置が異なることをブローと呼ぶ。たとえば、正解が 1234 で、回答が 1354 なら、出題者は「2 ヒット、1 ブロー」というヒントを与え、正解までこれを繰り返す。出題者と回答者は交代してゲームを行い、より少ない回答で正解を言い当てた方を勝ちとする。太郎君と花子さんは、ヒットの数とブローの数をその都度判断することが少し面倒に感じているようです。そんな二人のために、ヒットの数とブローの数が即座に分かるプログラムを作成してあげましょう。正解 r と回答 a を入力とし、ヒットの数とブローの数を出力するプログラムを作成してください。 r 、 a はそれぞれ 0 から 9 の数字 4 つからなる数字の列です。 Input 複数のデータセットの並びが入力として与えられます。入力の終わりはゼロふたつの行で示されます。各データセットとして、 r と a が空白区切りで１行に与えられます。データセットの数は 12000 を超えません。 Output 入力データセットごとに、ヒットの数とブローの数を１行に出力します。 Sample Input 1234 5678 1234 1354 1234 1234 1230 1023 0123 1234 0 0 Output for the Sample Input 0 0 2 1 4 0 1 3 0 3	36,137
Circles and Ray Problem 2次元平面上にそれぞれ互いに共通部分をもたない N 個の円が与えられる。また、円にはそれぞれ1から N までの番号が割り振られている。あなたは、端点が1番目の円の円周上にあるような半直線を任意の数だけ設置することができる。どの円も1本以上の半直線との共通部分を持っているようにするためには、最低何本の半直線を設置しなければならないかを求めなさい。 Input 入力は以下の形式で与えられる。 N x 1 y 1 r 1 x 2 y 2 r 2 ... x N y N r N 1行目に、1つの整数 N が与えられる。 2行目からの N 行のうち i 行目には i 番目の円のx座標、y座標、半径を表す3つの整数 x i , y i , r i が空白区切りで与えられる。 Constraints 2 ≤ N ≤ 16 -100 ≤ x i ≤ 100 (1 ≤ i ≤ N ) -100 ≤ y i ≤ 100 (1 ≤ i ≤ N ) 1 ≤ r i ≤ 100 (1 ≤ i ≤ N ) Output どの円も1本以上の半直線との共通部分を持っているようにするためには最低何本の半直線を設置しなければならないかを出力せよ。 Sample Input 1 3 0 0 2 3 3 1 6 1 1 Sample Output 1 1 Sample Input 2 4 1 2 3 12 2 2 7 6 2 1 9 3 Sample Output 2 2 Sample Input 3 5 0 0 5 0 10 1 10 0 1 -10 0 1 0 -10 1 Sample Output 3 4	36,138
Problem A: Infnity Maze Dr. Fukuoka has placed a simple robot in a two-dimensional maze. It moves within the maze and never goes out of the maze as there is no exit. The maze is made up of H × W grid cells as depicted below. The upper side of the maze faces north. Consequently, the right, lower and left sides face east, south and west respectively. Each cell is either empty or wall and has the coordinates of ( i , j ) where the north-west corner has (1, 1). The row i goes up toward the south and the column j toward the east. The robot moves on empty cells and faces north, east, south or west. It goes forward when there is an empty cell in front, and rotates 90 degrees to the right when it comes in front of a wall cell or on the edge of the maze. It cannot enter the wall cells. It stops right after moving forward by L cells. Your mission is, given the initial position and direction of the robot and the number of steps, to write a program to calculate the final position and direction of the robot. Input The input is a sequence of datasets. Each dataset is formatted as follows. H W L c 1,1 c 1,2 ... c 1, W . . . c H ,1 c H ,2 ... c H , W The first line of a dataset contains three integers H , W and L (1 ≤ H , W ≤ 100, 1 ≤ L ≤ 10 18 ). Each of the following H lines contains exactly W characters. In the i -th line, the j -th character c i,j represents a cell at ( i , j ) of the maze. " . " denotes an empty cell. " # " denotes a wall cell. " N ", " E ", " S ", " W " denote a robot on an empty cell facing north, east, south and west respectively; it indicates the initial position and direction of the robot. You can assume that there is at least one empty cell adjacent to the initial position of the robot. The end of input is indicated by a line with three zeros. This line is not part of any dataset. Output For each dataset, output in a line the final row, column and direction of the robot, separated by a single space. The direction should be one of the following: " N " (north), " E " (east), " S " (south) and " W " (west). No extra spaces or characters are allowed. Sample Input 3 3 10 E.. .#. ... 5 5 19 ####. ..... .#S#. ...#. #.##. 5 5 6 #.#.. #.... ##.#. #..S. #.... 5 4 35 ..## .... .##. .#S. ...# 0 0 0 Output for the Sample Input 1 3 E 4 5 S 4 4 E 1 1 N	36,139
Problem I: Sweet War There are two countries, Imperial Cacao and Principality of Cocoa. Two girls, Alice (the Empress of Cacao) and Brianna (the Princess of Cocoa) are friends and both of them love chocolate very much. One day, Alice found a transparent tube filled with chocolate balls (Figure I.1). The tube has only one opening at its top end. The tube is narrow, and the chocolate balls are put in a line. Chocolate balls are identified by integers 1, 2, . . ., $N$ where $N$ is the number of chocolate balls. Chocolate ball 1 is at the top and is next to the opening of the tube. Chocolate ball 2 is next to chocolate ball 1, . . ., and chocolate ball $N$ is at the bottom end of the tube. The chocolate balls can be only taken out from the opening, and therefore the chocolate balls must be taken out in the increasing order of their numbers. Figure I.1. Transparent tube filled with chocolate balls Alice visited Brianna to share the tube and eat the chocolate balls together. They looked at the chocolate balls carefully, and estimated that the $nutrition value$ and the $deliciousness$ of chocolate ball $i$ are $r_i$ and $s_i$, respectively. Here, each of the girls wants to maximize the sum of the deliciousness of chocolate balls that she would eat. They are sufficiently wise to resolve this conflict peacefully, so they have decided to play a game, and eat the chocolate balls according to the rule of the game as follows: Alice and Brianna have initial energy levels, denoted by nonnegative integers $A$ and $B$, respectively. Alice and Brianna takes one of the following two actions in turn: Pass : she does not eat any chocolate balls. She gets a little hungry $-$ specifically, her energy level is decreased by 1. She cannot pass when her energy level is 0. Eat : she eats the topmost chocolate ball $-$ let this chocolate ball $i$ (that is, the chocolate ball with the smallest number at that time). Her energy level is increased by $r_i$, the nutrition value of chocolate ball $i$ (and NOT decreased by 1). Of course, chocolate ball $i$ is removed from the tube. Alice takes her turn first. The game ends when all chocolate balls are eaten. You are a member of the staff serving for Empress Alice. Your task is to calculate the sums of deliciousness that each of Alice and Brianna can gain, when both of them play optimally. Input The input consists of a single test case. The test case is formatted as follows. $N$ $A$ $B$ $r_1$ $s_1$ $r_2$ $s_2$ . . . $r_N$ $s_N$ The first line contains three integers, $N$, $A$ and $B$. $N$ represents the number of chocolate balls. $A$ and $B$ represent the initial energy levels of Alice and Brianna, respectively. The following $N$ lines describe the chocolate balls in the tube. The chocolate balls are numbered from 1 to $N$, and each of the lines contains two integers, $r_i$ and $s_i$ for $1 \leq i \leq N$. $r_i$ and $s_i$ represent the nutrition value and the deliciousness of chocolate ball $i$, respectively. The input satisfies $1 \leq N \leq 150$, $0 \leq A, B, r_i \leq 10^9$, $0 \leq s_i$, and $\sum^N_{i=1} s_i \leq 150$ Output Output two integers that represent the total deliciousness that Alice and Brianna can obtain when they play optimally Sample Input 1 2 5 4 5 7 4 8 Sample Output 1 8 7 Sample Input 2 3 50 1 49 1 0 10 0 1 Sample Output 2 10 2 Sample Input 3 4 3 2 1 5 2 46 92 40 1 31 Sample Output 3 77 45 Sample Input 4 5 2 5 56 2 22 73 2 2 1 55 14 18 Sample Output 4 57 93	36,140
王様の視察とある国の偉い王様が、突然友好国の土地を視察することになった。その国は電車が有名で、王様はいろいろな駅を視察するという。電車の駅は52個あり、それぞれに大文字か小文字のアルファベット1文字の名前がついている（重なっている名前はない）。この電車の路線は環状になっていて、aの駅の次はbの駅、bの駅の次はcの駅と順に並んでいてz駅の次はA駅、その次はBの駅と順に進み、Z駅の次はa駅になって元に戻る。単線であり、逆方向に進む電車は走っていない。ある日、新聞社の記者が王様が訪れる駅の順番のリストを手に入れた。「dcdkIlkP…」最初にd駅を訪れ、次にc駅、次にd駅と順に訪れていくという。これで、偉い国の王様を追跡取材できると思った矢先、思わぬことが発覚した。そのリストは、テロ対策のため暗号化されていたのだ！記者の仲間が、その暗号を解く鍵を入手したという。早速この記者は鍵を譲ってもらい、リストの修正にとりかかった。鍵はいくつかの数字の列で構成されている。「3 1 4 5 3」この数字の意味するところは、はじめに訪れる駅は、リストに書いてある駅の3つ前の駅。 2番目に訪れる駅はリストの2番目の駅の前の駅、という風に、実際訪れる駅がリストの駅の何駅前かを示している。記者は修正に取りかかったが、訪れる駅のリストの数よりも、鍵の数の方が小さい、どうするのかと仲間に聞いたところ、最後の鍵をつかったら、またはじめの鍵から順に使っていけばよいらしい。そして記者はようやくリストを修正することができた。「abZfFijL…」これでもう怖い物は無いだろう、そう思った矢先、さらに思わぬ事態が発覚した。偉い王様は何日間も滞在し、さらにそれぞれの日程ごとにリストと鍵が存在したのだ。記者は上司から、すべてのリストを復号するように指示されたが、量が量だけに、彼一人では終わらない。あなたの仕事は彼を助け、このリストの復号を自動で行うプログラムを作成することである。 Input 入力は複数のデータセットから構成される。各データセットの形式は次の通りである。 n k1 k2... kn s n は鍵の数を表す整数であり、1以上 100 以下と仮定して良い。続く行には鍵のリストが記載されている。k i はi番目の鍵を示す。1以上52以下と仮定して良い。 sはアルファベット大文字・小文字からなる文字列で、訪れる駅のリストを示す。1文字以上100文字以下であると仮定して良い。 n=0 は入力の終わりを示す。これはデータセットには含めない。 Output 各データセットに対する復号されたリストを各1行に出力せよ。 Sample Input 2 1 2 bdd 3 3 2 1 DDDA 5 3 1 4 5 3 dcdkIlkP 0 Output for Sample Input abc ABCx abZfFijL	36,141
Problem D: Restrictive Filesystem あなたは新型記録媒体の開発チームに所属するプログラマーである．この記録媒体はデータの読み込み及び消去はランダムアクセスが可能である．一方，データを書き込むときは，常に先頭から順番にアクセスしていき，最初に見つかった空き領域にしか書き込むことができない．あなたはこの記録媒体用のファイルシステムの構築を始めた．このファイルシステムでは，記録媒体の制限から，データは先頭の空き領域から順に書き込まれる．書き込みの途中で別のデータが存在する領域に至った場合は，残りのデータをその後ろの空き領域から書き込んでいく．データの書き込みはセクタと呼ばれる単位で行われる．セクタには 0 から始まる番号が割り当てられており，この番号は記憶媒体上の物理的な位置を指す．セクタ番号は，記憶媒体の先頭から後方に向かって順に 0，1，2，3，… と割り当てられている．ファイルシステムには，書き込み，削除，セクタの参照という 3 つのコマンドが存在する．あなたの仕事はこのファイルシステムの挙動を再現した上で，参照コマンドが実行されたとき対象セクタにはどのファイルが配置されているか出力するプログラムを書くことである．なお，初期状態では記録媒体には何も書き込まれていない．例えば，Sample Input の最初の例を見てみよう．最初の命令では 0 という識別子を持ったサイズが 2 であるファイルを書き込む．初期状態では記録媒体には何も書き込まれていない，すなわち全てのセクタが空き領域であるから，先頭にある 2 つのセクタ，すなわち 0 番目のセクタと 1 番目のセクタに書き込みが行われる．したがって，書き込みの後の記憶媒体は次のようになっている．００空空空空空空 … 2 番目の命令によって，1 という識別子を持つファイルが 2 番目と 3 番目のセクタに書き込まれる．この後の記憶媒体の状態は次のようになる．００１１空空空空 … 3 番目の命令によって，0 の識別子を持つファイルが削除される．記憶媒体の状態は次のようになる．空空１１空空空空 … 4 番目の命令によって，2 という識別子を持つファイルを 0 番目，1 番目，4 番目，5 番目のセクタに書き込む．２２１１２２空空 … 最後の命令では，3 番目のセクタが参照される．いま，3 番目のセクタには 1 という識別子のファイルが配置されているので，あなたのプログラムは 1 と出力しなければならない． Input 入力は複数のデータセットからなる．各データセットは次の形式で与えられる． N Command 1 Command 2 ... Command N N は実行されるコマンドの数 (1 ≤ N ≤ 10,000)， Command i は i 番目に実行されるコマンドをそれぞれ表す．各コマンドは，コマンド名と 1 つまたは 2 つの引数からなる．コマンド名は 1 つの文字のみからなり，「W」，「D」，「R」のいずれかである．コマンドと引数の間，および引数と引数の間はそれぞれ 1 つのスペースで区切られる．「W」は書き込みのコマンドを表す．2 つの引数 I (0 ≤ I ≤ 10 9 ) と S (1 ≤ S ≤ 10 9 ) が与えられる．それぞれ，書き込むファイルの識別子とそのファイルを記憶するのに必要とするセクタの数を示す．「D」は削除のコマンドを表す．1 つの引数 I (0 ≤ I ≤ 10 9 ) が与えられる．削除するファイルの識別子を示す．「R」は参照のコマンドを表す．1 つの引数 P (0 ≤ P ≤ 10 9 ) が与えられる．参照するセクタの番号を示す． 10 9 よりも大きな番号を持つセクタにはアクセスする必要はないと仮定してよい．また，同じファイル識別子を持つファイルを複数回書き込むことはないことが保証されている．入力の終わりは，1 つの 0 を含む 1 行で示される． Output 各データセットについて，参照のコマンドが現れるごとに，そのコマンドによって参照されたファイルの識別子を 1 行に出力せよ．参照したセクタにファイルが書き込まれていなかった場合は，ファイル識別子の代わりに -1 を出力せよ．各データセットの後には空行を入れること． Sample Input 6 W 0 2 W 1 2 D 0 W 2 4 R 3 R 1 1 R 1000000000 0 Output for the Sample Input 1 2 -1	36,142
Problem E: Driving an Icosahedral Rover After decades of fruitless efforts, one of the expedition teams of ITO (Intersolar Tourism Organization) finally found a planet that would surely provide one of the best tourist attractions within a ten light-year radius from our solar system. The most attractive feature of the planet, besides its comfortable gravity and calm weather, is the area called Mare Triangularis . Despite the name, the area is not covered with water but is a great plane. Its unique feature is that it is divided into equilateral triangular sections of the same size, called trigons . The trigons provide a unique impressive landscape, a must for tourism. It is no wonder the board of ITO decided to invest a vast amount on the planet. Despite the expected secrecy of the staff, the Society of Astrogeology caught this information in no time, as always. They immediately sent their president's letter to the Institute of Science and Education of the Commonwealth Galactica claiming that authoritative academic inspections were to be completed before any commercial exploitation might damage the nature. Fortunately, astrogeologists do not plan to practice all the possible inspections on all of the trigons ; there are far too many of them. Inspections are planned only on some characteristic trigons and, for each of them, in one of twenty different scientific aspects. To accelerate building this new tourist resort, ITO's construction machinery team has already succeeded in putting their brand-new invention in practical use. It is a rover vehicle of the shape of an icosahedron , a regular polyhedron with twenty faces of equilateral triangles. The machine is customized so that each of the twenty faces exactly fits each of the trigons . Controlling the high-tech gyromotor installed inside its body, the rover can roll onto one of the three trigons neighboring the one its bottom is on. Figure E.1: The Rover on Mare Triangularis Each of the twenty faces has its own function. The set of equipments installed on the bottom face touching the ground can be applied to the trigon it is on. Of course, the rover was meant to accelerate construction of the luxury hotels to host rich interstellar travelers, but, changing the installed equipment sets, it can also be used to accelerate academic inspections. You are the driver of this rover and are asked to move the vehicle onto the trigon specified by the leader of the scientific commission with the smallest possible steps. What makes your task more difficult is that the designated face installed with the appropriate set of equipments has to be the bottom. The direction of the rover does not matter. Figure E.2:The Coordinate System Figure E.3: Face Numbering The trigons of Mare Triangularis are given two-dimensional coordinates as shown in Figure E.2. Like maps used for the Earth, the x axis is from the west to the east, and the y axis is from the south to the north. Note that all the trigons with its coordinates ( x , y ) has neighboring trigons with coordinates ( x - 1 , y ) and ( x + 1 , y ). In addition to these, when x + y is even, it has a neighbor ( x , y + 1); otherwise, that is, when x + y is odd, it has a neighbor ( x , y - 1). Figure E.3 shows a development of the skin of the rover. The top face of the development makes the exterior. That is, if the numbers on faces of the development were actually marked on the faces of the rover, they should been readable from its outside. These numbers are used to identify the faces. When you start the rover, it is on the trigon (0,0) and the face 0 is touching the ground. The rover is placed so that rolling towards north onto the trigon (0,1) makes the face numbered 5 to be at the bottom. As your first step, you can choose one of the three adjacent trigons , namely those with coordinates (-1,0), (1,0), and (0,1), to visit. The bottom will be the face numbered 4, 1, and 5, respectively. If you choose to go to (1,0) in the first rolling step, the second step can bring the rover to either of (0,0), (2,0), or (1,-1). The bottom face will be either of 0, 6, or 2, correspondingly. The rover may visit any of the trigons twice or more, including the start and the goal trigons , when appropriate. The theoretical design section of ITO showed that the rover can reach any goal trigon on the specified bottom face within a finite number of steps. Input The input consists of a number of datasets. The number of datasets does not exceed 50. Each of the datasets has three integers x , y , and n in one line, separated by a space. Here, (x,y) specifies the coordinates of the trigon to which you have to move the rover, and n specifies the face that should be at the bottom. The end of the input is indicated by a line containing three zeros. Output The output for each dataset should be a line containing a single integer that gives the minimum number of steps required to set the rover on the specified trigon with the specified face touching the ground. No other characters should appear in the output. You can assume that the maximum number of required steps does not exceed 100. Mare Triangularis is broad enough so that any of its edges cannot be reached within that number of steps. Sample Input 0 0 1 3 5 2 -4 1 3 13 -13 2 -32 15 9 -50 50 0 0 0 0 Output for the Sample Input 6 10 9 30 47 100	36,143
Weight 祖母が天秤を使っています。天秤は、二つの皿の両方に同じ目方のものを載せると釣合い、そうでない場合には、重い方に傾きます。10 個の分銅の重さは、軽い順に 1g, 2g, 4g, 8g, 16g, 32g, 64g, 128g, 256g, 512g です。祖母は、「1kg くらいまでグラム単位で量れるのよ。」と言います。「じゃあ、試しに、ここにあるジュースの重さを量ってよ」と言ってみると、祖母は左の皿にジュースを、右の皿に 8g と64g と128g の分銅を載せて釣合わせてから、「分銅の目方の合計は 200g だから、ジュースの目方は 200g ね。どう、正しいでしょう？」と答えました。左の皿に載せる品物の重さを与えるので、天秤で与えられた重みの品物と釣合わせるときに、右の皿に載せる分銅を軽い順に出力するプログラムを作成して下さい。ただし、量るべき品物の重さは、すべての分銅の重さの合計 (=1023g) 以下とします。 Input 複数のデータセットが与えられます。各データセットに、左の皿に載せる品物の重さが１行に与えられます。入力の最後まで処理して下さい。データセットの数は 50 を超えません。 Output 各データセットに対して、右の皿に載せる分銅（昇順）を１つの空白で区切って、１行に出力して下さい。 Sample Input 5 7 127 Output for the Sample Input 1 4 1 2 4 1 2 4 8 16 32 64 Hint 分銅の重さは 2 の n 乗 ( n = 0, 1, .... 9 )g です。	36,144
IOIOI 問題整数 n (1 ≤ n ) に対し, n + 1 個の I と n 個の O を I から始めて交互に並べてできる文字列を P n とする.ここで I と O はそれぞれ英大文字のアイとオーである. P 1 IOI P 2 IOIOI P 3 IOIOIOI . . . P n IOIOIO ... OI ( O が n 個) 図 1-1 本問で考える文字列 P n 整数 n と, I と O のみからなる文字列 s が与えられた時, s の中に P n が何ヶ所含まれているかを出力するプログラムを作成せよ. 例 n が 1, s が OOIOIOIOIIOII の場合, P 1 は IOI であり,下図 1-2 に示した 4ヶ所に含まれている.よって,出力は 4 である. OO IOI OIOIIOII OOIO IOI OIIOII OOIOIO IOI IOII OOIOIOIOI IOI I 図 1-2 n が 1, s が OOIOIOIOIIOII の場合の例 n が 2, s が OOIOIOIOIIOII の場合, P 2 は IOIOI であり,下図 1-3 に示した 2ヶ所に含まれている.よって,出力は 2 である. OO IOIOI OIIOII OOIO IOIOI IOII 図 1-3 n が 2, s が OOIOIOIOIIOII の場合の例入力入力は複数のデータセットからなる．各データセットは以下の形式で与えられる． 1 行目には整数 n (1 ≤ n ≤ 1000000) が書かれている. 2 行目には整数 m (1 ≤ m ≤ 1000000) が書かれている. m は s の文字数を表す. 3 行目には文字列 s が書かれている. s は I と O のみからなる. 全ての採点用データで, 2 n + 1 ≤ m である.採点用データのうち, 配点の 50% 分については, n ≤ 100, m ≤ 10000 を満たす. n が 0 のとき入力の終了を示す. データセットの数は 10 を超えない．出力データセットごとに,文字列 s に文字列 P n が何ヶ所含まれるかを表す 1 つの整数を1 行に出力する. s に P n が含まれていない場合は,整数として 0 を出力せよ. 入出力例入力例 1 13 OOIOIOIOIIOII 2 13 OOIOIOIOIIOII 0 出力例 4 2 上記問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	36,145
Problem A: Lunch Problem ある日、川林くんは学食で昼食を食べようとしています。学食にはAランチ、Bランチ、Cランチの3種類の日替わりのランチメニューがあります。川林くんは食いしん坊なので3種類の日替わりのランチメニューをすべて1つずつ食べたいと思っています。しかし、川林くんは健康に気を使って摂取するカロリーの合計が最小になるように1種類のランチメニューを我慢し、異なる2種類のランチメニューを食べることにしました。ある日のAランチ、Bランチ、Cランチのカロリーが与えられた時、川林くんが我慢することになるランチメニューを求めてください。 Input 入力は以下の形式で与えられる。 $a$ $b$ $c$ 3つの整数$a$, $b$, $c$が空白区切りで与えられる。それぞれ、ある日のAランチ、Bランチ、Cランチのカロリーを表している。 Constraints 入力は以下の条件を満たす。 $1 \leq a, b, c \leq 5000 $ $a \neq b, b \neq c, c \neq a$ Output 川林くんが我慢することになるメニュー名を1行に出力せよ。 Aランチを我慢する場合は"A" Bランチを我慢する場合は"B" Cランチを我慢する場合は"C" と出力せよ。 Sample Input 1 1000 900 850 Sample Output 1 A Sample Input 2 1000 800 1200 Sample Output 2 C	36,146
バドミントン A君、Bさん、C君で久しぶりに遊ぶことになりました。 A君とBさんがプレイヤー、C君が審判になりバドミントンのシングルスのゲームをしました。3人で決めたルールは以下の通りです。 3 ゲームを行います。 11 点を先取した人が、そのゲームの勝者となります。第 1 ゲームの最初のサーブはA君から始まりますが、次のサーブは直前のポイントを取った人が行います。第 2 ゲーム、第 3 ゲームは前のゲームを取った人が最初のサーブを行います。 10 - 10 になって以降は 2 点差をつけた人が勝者となります。全てのゲームが終わり、得点を見ようとしたのですが、審判のC君が得点を記録するのを忘れていました。しかし、サーブを打った人をきちんと記録していました。サーブ順の記録から得点を計算するプログラムを作成してください。ただし、二人が打ったサーブの回数の合計は 100 以下とし、サーブ順の記録は、サーブを打った人を表す "A" または "B" の文字列で表されます。 Input 複数のデータセットの並びが入力として与えられます。入力の終わりはゼロひとつの行で示されます。各データセットは以下の形式で与えられます。 record 1 record 2 record 3 i 行目に第 i ゲームのサーブ順を表す文字列が与えられます。データセットの数は 20 を超えません。 Output データセット毎に、 i 行目に第 i ゲームのA君の得点とBさんの得点を空白区切りで出力してください。 Sample Input ABAABBBAABABAAABBAA AABBBABBABBAAABABABAAB BABAABAABABABBAAAB AABABAAABBAABBBABAA AAAAAAAAAAA ABBBBBBBBBB 0 Output for the Sample Input 11 8 10 12 11 7 11 8 11 0 0 11	36,147
フクロモモンガ(Sugar Glider) フクロモモンガのJOI 君が住んでいる森にはユーカリの木が $N$ 本生えており，それらの木には1 から $N$ の番号がついている．木 $i$ の高さは $H_i$ メートルである． JOI 君が相互に直接飛び移ることのできる木の組が $M$ 組あり，各組の木の間を飛び移るためにかかる時間が定まっている．JOI 君が木の間を飛び移っている間は，地面からの高さが1 秒あたり1 メートル下がる．すなわち，JOI 君の現在の地面からの高さが $h$ メートル，木の間を飛び移るためにかかる時間が $t$ 秒であるとき，飛び移った後の地面からの高さは $h - t$ メートルとなる．ただし，$h - t$ が0 よりも小さくなる場合や行き先の木の高さよりも大きくなる場合は飛び移ることができない．さらに，JOI 君は木の側面を上下に移動することによって，地面からの高さを0 メートルから今いる木の高さの範囲で増減させることができる．JOI 君が地面からの高さを1 メートル増加または減少させるためには1 秒の時間がかかる． JOI 君は，木1 の高さ$X$ メートルの位置から木$N$ の頂上(高さ$H_N$ メートルの位置) に行こうとしており，そのためにかかる時間の最小値を知りたい．課題各木の高さと，JOI 君が直接飛び移ることができる木の組の情報と，最初JOI 君がいる場所の高さが与えられる．木 $N$ の頂上に行くためにかかる時間の最小値を求めるプログラムを作成せよ. 入力標準入力から以下のデータを読み込め． 1 行目には，整数 $N, M, X$ が空白を区切りとして書かれている．これは，木の本数が $N$ 本，移動できる木の組が $M$ 組あり，最初JOI 君が木1 の高さ $X$ メートルの位置にいることを表す．続く $N$ 行のうちの $i$ 行目$(1 \leq i \leq N)$ には，整数 $H_i$ が書かれている．これは，木 $i$ の高さが $H_i$ メートルであることを表す．続く$M$ 行のうちの $j$ 行目$(1 \leq j \leq M)$ には，整数 $A_j, B_j, T_j$ $(1 \leq A_j \leq N, 1 \leq B_j \leq N, A_j \ne B_j)$ が空白を区切りとして書かれている．これは，木 $A_j$ と木 $B_j$ の間を相互に $T_j$ 秒で飛び移ることができることを表している．また，$1 \leq j < k \leq M$ ならば，$(A_j, B_j) \ne (A_k, B_k)$ および$(A_j, B_j) \ne (B_k, A_k)$ を満たす．出力標準出力に，木1 の高さ $X$ メートルの位置から木 $N$ の頂上に行くためにかかる時間の最小値を秒単位で表す整数を1 行で出力せよ．ただし，そのような方法がない場合は代わりに -1 を出力せよ．制限すべての入力データは以下の条件を満たす． $2 \leq N \leq 100000$ $1 \leq M \leq 300000$ $1 \leq H_i \leq 1000000000 (1 \leq i \leq N)$ $1 \leq T_j \leq 1000000000 (1 \leq j \leq M)$ $0 \leq X \leq H_1$ 入出力例入力例 1 5 5 0 50 100 25 30 10 1 2 10 2 5 50 2 4 20 4 3 1 5 4 20 出力例 1 110 例えば，以下のように移動すればよい． 1. 木1 を50 メートル登る． 2. 木1 から木2 に飛び移る． 3. 木2 から木4 に飛び移る． 4. 木4 から木5 に飛び移る． 5. 木5 を10 メートル登る．入力例 2 2 1 0 1 1 1 2 100 出力例 2 -1 JOI 君は木1 から木2 に飛び移ることができない．入力例 3 4 3 30 50 10 20 50 1 2 10 2 3 10 3 4 10 出力例 3 100 問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	36,148
Problem D: Separate Points Numbers of black and white points are placed on a plane. Let's imagine that a straight line of infinite length is drawn on the plane. When the line does not meet any of the points, the line divides these points into two groups. If the division by such a line results in one group consisting only of black points and the other consisting only of white points, we say that the line "separates black and white points". Let's see examples in Figure 3. In the leftmost example, you can easily find that the black and white points can be perfectly separated by the dashed line according to their colors. In the remaining three examples, there exists no such straight line that gives such a separation. Figure 3: Example planes In this problem, given a set of points with their colors and positions, you are requested to decide whether there exists a straight line that separates black and white points. Input The input is a sequence of datasets, each of which is formatted as follows. n m x 1 y 1 . . . x n y n x n +1 y n +1 . . . x n + m y n + m The first line contains two positive integers separated by a single space; n is the number of black points, and m is the number of white points. They are less than or equal to 100. Then n + m lines representing the coordinates of points follow. Each line contains two integers x i and y i separated by a space, where ( x i , y i ) represents the x -coordinate and the y -coordinate of the i -th point. The color of the i -th point is black for 1 ≤ i ≤ n , and is white for n + 1 ≤ i ≤ n + m . All the points have integral x - and y -coordinate values between 0 and 10000 inclusive. You can also assume that no two points have the same position. The end of the input is indicated by a line containing two zeros separated by a space. Output For each dataset, output " YES " if there exists a line satisfying the condition. If not, output " NO ". In either case, print it in one line for each input dataset. Sample Input 3 3 100 700 200 200 600 600 500 100 500 300 800 500 3 3 100 300 400 600 400 100 600 400 500 900 300 300 3 4 300 300 500 300 400 600 100 100 200 900 500 900 800 100 1 2 300 300 100 100 500 500 1 1 100 100 200 100 2 2 0 0 500 700 1000 1400 1500 2100 2 2 0 0 1000 1000 1000 0 0 1000 3 3 0 100 4999 102 10000 103 5001 102 10000 102 0 101 3 3 100 100 200 100 100 200 0 0 400 0 0 400 3 3 2813 1640 2583 2892 2967 1916 541 3562 9298 3686 7443 7921 0 0 Output for the Sample Input YES NO NO NO YES YES NO NO NO YES	36,149
F : Todaiji / 東大寺 Problem づいあ君は旅行が大好きである。奈良旅行に訪れたづいあ君は、東大寺にある柱の穴をくぐることにした。しかし、づいあ君は最近太りだしたため、穴に引っかかってしまうかもしれない。そこでづいあ君は、どこまで太っても大丈夫かを調べるプログラムを書くことにした。簡単のため問題は平面上で考える。穴は2本の折れ線で、づいあ君は円で表すこととする。折れ線 1 は点 (0,0) が始点、点 (1000,0) が終点である。折れ線 2 は点 (0,1000) が始点、点 (1000,1000) が終点である。づいあ君の全身が x < 0 の領域にある状態から、2 本の折れ線の間を通り、 x > 1000 の領域にづいあ君の全身が出た状態に到達できるような最大の直径を求めてほしい。通過する際の経路は自由であり、円が折れ線に接しても良い。 Input 入力は次のような形式で与えられる。 N 1 x 11 y 11 x 12 y 12 ... x 1N1 y 1N1 N 2 x 21 y 21 x 22 y 22 ... x 2N2 y 2N2 N 1 は1つ目の折れ線を構成する点の数である。 x 1i , y 1i は、1つ目の折れ線を構成する i 番目の点の座標である。( x 1i , y 1i ) と ( x 1(i+1) , y 1(i+1) ) が結ばれる。 (0,0) と ( x 11 , y 11 )、( x 1N1 , y 1N1 ) と (1000,0) がそれぞれ線で結ばれる。 2つ目の折れ線についても折れ線1と同様の形式で入力される。ただし、( x 21 , y 21 ) と結ばれるのは (0,1000)、( x 2N2 , y 2N2 ) と結ばれるのは (1000,1000) である。 Constraints 入力は全て整数である。 1 ≦ N 1 , N 2 ≦ 50 0 ≦ x ij , y ij ≦ 1000 x ij ≦ x i(j+1) 折れ線は自分自身と交わらない。 2 本の折れ線は交わらない。 Output 2 本の折れ線の間を通過できる、づいあ君の体の最大の直径を1行で出力せよ。10 -6 までの誤差は許される。 Samples Sapmle Input 1 2 300 300 700 300 2 300 700 700 700 Sapmle Output 1 400.0000000000 Sapmle Input 2 31 53 334 96 201 99 129 114 365 123 39 186 257 195 247 233 335 256 79 302 217 404 302 411 222 428 422 433 388 441 443 468 309 497 408 518 218 537 361 538 193 541 447 580 16 606 185 610 178 737 421 754 210 805 418 849 416 876 262 878 220 948 207 28 7 919 89 640 145 656 152 963 204 558 252 630 269 690 325 629 357 583 454 593 523 648 538 949 541 821 559 655 581 614 593 877 607 571 631 817 682 942 776 529 810 606 813 598 834 778 838 999 910 661 920 824 982 517 987 689 Sapmle Output 2 114.7257599670 サンプル 2 を図示するとこのようになる。	36,150
Max Score: $1500$ Points Problem Statement Huge kingdom: $Atcoder$ contains $N$ towns and $N-1$ roads. This kingdom is connected. You have to detect the kingdom's road. In order to detect, You can ask this form of questions. You can output a string $S$. Length of $S$ must be $N$ and The character of string $S$ must be represented by '$0$' or '$1$'. Computer paint the towns with white or black according to the character string you output. If $i$-th character of $S$ is '0', computer paint town $i$ white. If $i$-th character of $S$ is '1', computer paint town $i$ black. Please consider an undirected graph $G$. For each edge, computer do the following processing: If both ends painted black, computer adds this edge to $G$. Computer returns value $x$: sum of "diameter of tree"$^2$ about each connected components. For example, when $S$="11001111" and the kingdom's structure is this, computer returns 10. Please detect the structure of $Atcoder$ as few questions as possible. Input, Output This is a reactive problem. The first input is as follows: $N$ $N$ is number of towns in $Atcoder$. Next, you can ask questions. The question must be in the form as follows: ? $S$ $S$ is a string. The mean of $S$ written in the problem statement. Length of $S$ must be $N$. The answer of question is as follows: $x$ The mean of $x$ written in the problem statement. Finally, your program must output as follows: ! $(a_1,b_1)$ $(a_2,b_2)$ $(a_3,b_3)$ … $(a_{N-1},b_{N-1})$ This output means your program detects all roads of $Atcoder$. $(a_i,b_i)$ means there is a road between $a_i$ and $b_i$. You can output roads any order, but you must output the answer on a single line. Constraints $N$=200 $Atcoder$ contains $N-1$ roads and this kingdom is connected. All cases were made randomly. Scoring Let the number of questions be $L$. If $L > 20000$, $score$ = $0$ points If $18000 < L ≦ 20000$, $score$ = $200$ points If $5000 < L ≦ 18000$, $score$ = $650-L/40$ points If $4000 < L ≦ 5000$, $score$ = $800-L/20$ points If $2000 < L ≦ 4000$, $score$ = $1400-L/5$ points If $1200 < L ≦ 2000$, $score$ = $1500-L/4$ points If $700 < L ≦ 1200$, $score$ = $1850-L/2$ points If $L ≦ 700$, $score$ = $1500$ points There is $5$ cases, so points of each case is $score/5$. Sample Input This case is $N=4$. This case is not include because this is not $N=200$. N=4 0 1 1 2 1 3 Sample Output Sample interaction is as follows: Input from computer Output 4 ? 1111 4 ? 1101 4 ? 1001 0 ? 1100 1 ? 1011 0 ! (0,1) (1,2) (1,3) In this sample, structure of $Atcoder$ is as follows: This question is not always meaningful.	36,151
Problem C: K Poker Description 時は200X年、K大学で活動する謎のサークルKはその大学の文化祭の最中にK東4Fで彼らが作成した新たなゲーム、Kポーカーを発表した。このゲームは一見すると普通のポーカーであるが、カードに基本点という要素をつけてポーカーをより奥の深いゲームにしたものである。カードの基本点はそれぞれのカードに書かれている絵柄によって決まり、手札の点数は手札にある5枚の基本点の合計に手札の役の倍率を掛けたものになる。この基本点を導入した事により、例えばフルハウスなどの強い役を作ったとしても基本点が0であればブタと同様に扱われてしまい、ワンペアに負けることさえある。それ以外のルールは通常のポーカーと同じである。このKポーカーをPCに移植しようと思ったあなたは手札の点数を計算するプログラムを書く事にした。なおこのゲームは18歳未満の人はプレイ出来ない。 Input 入力は複数のテストケースからなる。各テストケースの最初の行にはチェックする手札の数Nが書かれている。次の4行には13個の整数が並びカードの基本点が1-13の順に並んで書かれている。4行のスーツは上から順にスペード、クローバー、ハート、ダイヤの順に並んでいる。次の行には9個の整数が並び、順にワンペア、ツーペア、スリーカード、ストレート、フラッシュ、フルハウス、フォーカード、ストレートフラッシュ、ロイヤルストレートフラッシュの倍率を表している。役の倍率は必ず昇順となっている。ブタ(役無し、ノーペア)の倍率は常に0である。次のN行には手札を表す5個の長さ2の異なる文字列が並んでいる。1文字目はカードの数値を表し,A,2,3,4,5,6,7,8,9,T,J,Q,Kのいずれかである。2文字目はカードのスーツを表し、S,C,H,Dのいずれかである。各アルファベットはAはエース、Tは10、Jはジャック、Qはクイーン、Kはキング、Sはスペード、Cはクローバー、Hはハート、Dはダイヤを表す。入力の数値は全て[0,10000]の範囲に収まっている。入力はEOFで終わる。 Output 各手札の点数を1行ずつ出力せよ。連続する2つのテストケースの間には空行を1つ入れること。役については wikipediaのポーカーのページを参照のこと。なお、ストレートはエースとキングをまたぐ場合があるが、手札が10,ジャック、クイーン、キング、エースの場合にのみストレートとみなされる。 Sample Input 3 0 1 0 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 2 0 1 1 0 1 1 1 0 0 0 0 5 5 3 1 1 1 0 1 0 0 1 0 3 0 2 1 1 2 4 5 10 20 50 100 7H 6H 2H 5H 3H 9S 9C 9H 8H 8D KS KH QH JD TS 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 3 4 5 6 7 8 9 AS 3D 2C 5D 6H 6S 6C 7D 8H 9C TS TD QC JD JC KD KH KC AD 2C 3D 4H 6D 5H 7C 2S KS QS AS JS TS TD JD JC TH 8H 8D TC 8C 8S 4S 5S 3S 7S 6S KD QD JD TD AD Output for Sample Input 25 0 14 0 5 10 15 20 25 30 35 40 45	36,152
Score : 200 points Problem Statement You are given an integer sequence A of length N . Find the maximum absolute difference of two elements (with different indices) in A . Constraints 2 \leq N \leq 100 1 \leq A_i \leq 10^9 All values in input are integers. Input Input is given from Standard Input in the following format: N A_1 A_2 ... A_N Output Print the maximum absolute difference of two elements (with different indices) in A . Sample Input 1 4 1 4 6 3 Sample Output 1 5 The maximum absolute difference of two elements is A_3-A_1=6-1=5 . Sample Input 2 2 1000000000 1 Sample Output 2 999999999 Sample Input 3 5 1 1 1 1 1 Sample Output 3 0	36,153
Score : 400 points Problem Statement You have a sequence A composed of N positive integers: A_{1}, A_{2}, \cdots, A_{N} . You will now successively do the following Q operations: In the i -th operation, you replace every element whose value is B_{i} with C_{i} . For each i (1 \leq i \leq Q) , find S_{i} : the sum of all elements in A just after the i -th operation. Constraints All values in input are integers. 1 \leq N, Q, A_{i}, B_{i}, C_{i} \leq 10^{5} B_{i} \neq C_{i} Input Input is given from Standard Input in the following format: N A_{1} A_{2} \cdots A_{N} Q B_{1} C_{1} B_{2} C_{2} \vdots B_{Q} C_{Q} Output Print Q integers S_{i} to Standard Output in the following format: S_{1} S_{2} \vdots S_{Q} Note that S_{i} may not fit into a 32 -bit integer. Sample Input 1 4 1 2 3 4 3 1 2 3 4 2 4 Sample Output 1 11 12 16 Initially, the sequence A is 1,2,3,4 . After each operation, it becomes the following: 2, 2, 3, 4 2, 2, 4, 4 4, 4, 4, 4 Sample Input 2 4 1 1 1 1 3 1 2 2 1 3 5 Sample Output 2 8 4 4 Note that the sequence A may not contain an element whose value is B_{i} . Sample Input 3 2 1 2 3 1 100 2 100 100 1000 Sample Output 3 102 200 2000	36,154
Score : 700 points Problem Statement Takahashi is playing with N cards. The i -th card has an integer X_i on it. Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions: The integers on the two cards are the same. The sum of the integers on the two cards is a multiple of M . Find the maximum number of pairs that can be created. Note that a card cannot be used in more than one pair. Constraints 2≦N≦10^5 1≦M≦10^5 1≦X_i≦10^5 Input The input is given from Standard Input in the following format: N M X_1 X_2 ... X_N Output Print the maximum number of pairs that can be created. Sample Input 1 7 5 3 1 4 1 5 9 2 Sample Output 1 3 Three pairs (3,2), (1,4) and (1,9) can be created. It is possible to create pairs (3,2) and (1,1) , but the number of pairs is not maximized with this. Sample Input 2 15 10 1 5 6 10 11 11 11 20 21 25 25 26 99 99 99 Sample Output 2 6	36,155
Score : 100 points Problem Statement In an electric circuit, when two resistors R_1 and R_2 are connected in parallel, the equivalent resistance R_3 can be derived from the following formula: \frac{1}{R_1} + \frac{1}{R_2} = \frac{1}{R_3} Given R_1 and R_2 , find R_3 . Constraints 1 \leq R_1, R_2 \leq 100 R_1 and R_2 are integers. Input The input is given from Standard Input in the following format: R_1 R_2 Output Print the value of R_3 . The output is considered correct if the absolute or relative error is at most 10^{-6} . Sample Input 1 2 3 Sample Output 1 1.2000000000 Sample Input 2 100 99 Sample Output 2 49.7487437186	36,156
Selection Sort Write a program of the Selection Sort algorithm which sorts a sequence A in ascending order. The algorithm should be based on the following pseudocode: SelectionSort(A) 1 for i = 0 to A.length-1 2 mini = i 3 for j = i to A.length-1 4 if A[j] < A[mini] 5 mini = j 6 swap A[i] and A[mini] Note that, indices for array elements are based on 0-origin. Your program should also print the number of swap operations defined in line 6 of the pseudocode in the case where i ≠ mini. Input The first line of the input includes an integer N , the number of elements in the sequence. In the second line, N elements of the sequence are given separated by space characters. Output The output consists of 2 lines. In the first line, please print the sorted sequence. Two contiguous elements of the sequence should be separated by a space character. In the second line, please print the number of swap operations. Constraints 1 ≤ N ≤ 100 Sample Input 1 6 5 6 4 2 1 3 Sample Output 1 1 2 3 4 5 6 4 Sample Input 2 6 5 2 4 6 1 3 Sample Output 2 1 2 3 4 5 6 3	36,157
Score : 1500 points Problem Statement You are given a tree with N vertices numbered 1, 2, ..., N . The i -th edge connects Vertex a_i and Vertex b_i . You are also given a string S of length N consisting of 0 and 1 . The i -th character of S represents the number of pieces placed on Vertex i . Snuke will perform the following operation some number of times: Choose two pieces the distance between which is at least 2 , and bring these pieces closer to each other by 1 . More formally, choose two vertices u and v , each with one or more pieces, and consider the shortest path between them. Here the path must contain at least two edges. Then, move one piece from u to its adjacent vertex on the path, and move one piece from v to its adjacent vertex on the path. By repeating this operation, Snuke wants to have all the pieces on the same vertex. Is this possible? If the answer is yes, also find the minimum number of operations required to achieve it. Constraints 2 \leq N \leq 2000 \|S\| = N S consists of 0 and 1 , and contains at least one 1 . 1 \leq a_i, b_i \leq N(a_i \neq b_i) The edges (a_1, b_1), (a_2, b_2), ..., (a_{N - 1}, b_{N - 1}) forms a tree. Input Input is given from Standard Input in the following format: N S a_1 b_1 a_2 b_2 : a_{N - 1} b_{N - 1} Output If it is impossible to have all the pieces on the same vertex, print -1 . If it is possible, print the minimum number of operations required. Sample Input 1 7 0010101 1 2 2 3 1 4 4 5 1 6 6 7 Sample Output 1 3 We can gather all the pieces in three operations as follows: Choose the pieces on Vertex 3 and 5 . Choose the pieces on Vertex 2 and 7 . Choose the pieces on Vertex 4 and 6 . Sample Input 2 7 0010110 1 2 2 3 1 4 4 5 1 6 6 7 Sample Output 2 -1 Sample Input 3 2 01 1 2 Sample Output 3 0	36,158
Score : 300 points Problem Statement The commonly used bills in Japan are 10000 -yen, 5000 -yen and 1000 -yen bills. Below, the word "bill" refers to only these. According to Aohashi, he received an otoshidama (New Year money gift) envelope from his grandfather that contained N bills for a total of Y yen, but he may be lying. Determine whether such a situation is possible, and if it is, find a possible set of bills contained in the envelope. Assume that his grandfather is rich enough, and the envelope was large enough. Constraints 1 ≤ N ≤ 2000 1000 ≤ Y ≤ 2 × 10^7 N is an integer. Y is a multiple of 1000 . Input Input is given from Standard Input in the following format: N Y Output If the total value of N bills cannot be Y yen, print -1 -1 -1 . If the total value of N bills can be Y yen, let one such set of bills be " x 10000 -yen bills, y 5000 -yen bills and z 1000 -yen bills", and print x , y , z with spaces in between. If there are multiple possibilities, any of them may be printed. Sample Input 1 9 45000 Sample Output 1 4 0 5 If the envelope contained 4 10000 -yen bills and 5 1000 -yen bills, he had 9 bills and 45000 yen in total. It is also possible that the envelope contained 9 5000 -yen bills, so the output 0 9 0 is also correct. Sample Input 2 20 196000 Sample Output 2 -1 -1 -1 When the envelope contained 20 bills in total, the total value would be 200000 yen if all the bills were 10000 -yen bills, and would be at most 195000 yen otherwise, so it would never be 196000 yen. Sample Input 3 1000 1234000 Sample Output 3 14 27 959 There are also many other possibilities. Sample Input 4 2000 20000000 Sample Output 4 2000 0 0	36,159
Score : 100 points Problem Statement There are N items, numbered 1, 2, \ldots, N . For each i ( 1 \leq i \leq N ), Item i has a weight of w_i and a value of v_i . Taro has decided to choose some of the N items and carry them home in a knapsack. The capacity of the knapsack is W , which means that the sum of the weights of items taken must be at most W . Find the maximum possible sum of the values of items that Taro takes home. Constraints All values in input are integers. 1 \leq N \leq 100 1 \leq W \leq 10^9 1 \leq w_i \leq W 1 \leq v_i \leq 10^3 Input Input is given from Standard Input in the following format: N W w_1 v_1 w_2 v_2 : w_N v_N Output Print the maximum possible sum of the values of items that Taro takes home. Sample Input 1 3 8 3 30 4 50 5 60 Sample Output 1 90 Items 1 and 3 should be taken. Then, the sum of the weights is 3 + 5 = 8 , and the sum of the values is 30 + 60 = 90 . Sample Input 2 1 1000000000 1000000000 10 Sample Output 2 10 Sample Input 3 6 15 6 5 5 6 6 4 6 6 3 5 7 2 Sample Output 3 17 Items 2, 4 and 5 should be taken. Then, the sum of the weights is 5 + 6 + 3 = 14 , and the sum of the values is 6 + 6 + 5 = 17 .	36,160
Problem E: Autocorrelation Function Nathan O. Davis is taking a class of signal processing as a student in engineering. Today’s topic of the class was autocorrelation. It is a mathematical tool for analysis of signals represented by functions or series of values. Autocorrelation gives correlation of a signal with itself. For a continuous real function f ( x ), the autocorrelation function R f ( r ) is given by where r is a real number. The professor teaching in the class presented an assignment today. This assignment requires students to make plots of the autocorrelation functions for given functions. Each function is piecewise linear and continuous for all real numbers. The figure below depicts one of those functions. Figure 1: An Example of Given Functions The professor suggested use of computer programs, but unfortunately Nathan hates programming. So he calls you for help, as he knows you are a great programmer. You are requested to write a program that computes the value of the autocorrelation function where a function f ( x ) and a parameter r are given as the input. Since he is good at utilization of existing software, he could finish his assignment with your program. Input The input consists of a series of data sets. The first line of each data set contains an integer n (3 ≤ n ≤ 100) and a real number r (-100 ≤ r ≤ 100), where n denotes the number of endpoints forming sub-intervals in the function f ( x ), and r gives the parameter of the autocorrelation function R f ( r ). The i -th of the following n lines contains two integers x i (-100 ≤ x i ≤ 100) and y i (-50 ≤ y i ≤ 50), where ( x i , y i ) is the coordinates of the i -th endpoint. The endpoints are given in increasing order of their x -coordinates, and no couple of endpoints shares the same x -coordinate value. The y -coordinates of the first and last endpoints are always zero. The end of input is indicated by n = r = 0. This is not part of data sets, and hence should not be processed. Output For each data set, your program should print the value of the autocorrelation function in a line. Each value may be printed with an arbitrary number of digits after the decimal point, but should not contain an error greater than 10 -4 . Sample Input 3 1 0 0 1 1 2 0 11 1.5 0 0 2 7 5 3 7 8 10 -5 13 4 15 -1 17 3 20 -7 23 9 24 0 0 0 Output for the Sample Input 0.166666666666667 165.213541666667	36,161
Score : 400 points Problem Statement Snuke has a string S consisting of three kinds of letters: a , b and c . He has a phobia for palindromes, and wants to permute the characters in S so that S will not contain a palindrome of length 2 or more as a substring. Determine whether this is possible. Constraints 1 \leq \|S\| \leq 10^5 S consists of a , b and c . Input Input is given from Standard Input in the following format: S Output If the objective is achievable, print YES ; if it is unachievable, print NO . Sample Input 1 abac Sample Output 1 YES As it stands now, S contains a palindrome aba , but we can permute the characters to get acba , for example, that does not contain a palindrome of length 2 or more. Sample Input 2 aba Sample Output 2 NO Sample Input 3 babacccabab Sample Output 3 YES	36,162
PLAY in BASIC One sunny day, Dick T. Mustang found an ancient personal computer in the closet. He brought it back to his room and turned it on with a sense of nostalgia, seeing a message coming on the screen: READY? Yes. BASIC. BASIC is a programming language designed for beginners, and was widely used from 1980's to 1990's. There have been quite a few BASIC dialects. Some of them provide the PLAY statement, which plays music when called with a string of a musical score written in Music Macro Language (MML). Dick found this statement is available on his computer and accepts the following commands in MML: Notes: Cn, C+n, C-n, Dn, D+n, D-n, En,...,... (n = 1,2,4,8,16,32,64,128 + dots) Each note command consists of a musical note followed by a duration specifier. Each musical note is one of the seven basic notes: 'C', 'D', 'E', 'F', 'G', 'A', and 'B'. It can be followed by either '+' (indicating a sharp) or '-' (a flat). The notes 'C' through 'B' form an octave as depicted in the figure below. The octave for each command is determined by the current octave, which is set by the octave commands as described later. It is not possible to play the note 'C-' of the lowest octave (1) nor the note 'B+' of the highest octave (8). Each duration specifier is basically one of the following numbers: '1', '2', '4', '8', '16', '32', '64', and '128', where '1' denotes a whole note, '2' a half note, '4' a quarter note, '8' an eighth note, and so on. This specifier is optional ; when omitted, the duration will be the default one set by the L command (which is described below). In addition, duration specifiers can contain dots next to the numbers. A dot adds the half duration of the basic note. For example, '4.' denotes the duration of '4' (a quarter) plus '8' (an eighth, i.e. half of a quarter), or as 1.5 times long as '4'. It is possible that a single note has more than one dot, where each extra dot extends the duration by half of the previous one. For example, '4..' denotes the duration of '4' plus '8' plus '16', '4...' denotes the duration of '4' plus '8' plus '16' plus '32', and so on. The duration extended by dots cannot be shorter than that of '128' due to limitation of Dick's computer; therefore neither '128.' nor '32...' will be accepted. The dots specified without the numbers extend the default duration. For example, 'C.' is equivalent to 'C4.' when the default duration is '4'. Note that 'C4C8' and 'C4.' are unequivalent ; the former contains two distinct notes, while the latter just one note. Rest: Rn (n = 1,2,4,8,16,32,64,128 + dots) The R command rests for the specified duration. The duration should be specified in the same way as the note commands, and it can be omitted, too. Note that 'R4R8' and 'R4.' are equivalent , unlike 'C4C8' and 'C4.', since the both rest for the same duration of '4' plus '8'. Octave: On (n = 1-8), <, > The O command sets the current octave to the specified number. '>' raises one octave up, and '<' drops one down. It is not allowed to set the octave beyond the range from 1 to 8 by these commands. The octave is initially set to 4. Default duration: Ln (n = 1,2,4,8,16,32,64,128) The L command sets the default duration. The duration should be specified in the same way as the note commands, but cannot be omitted nor followed by dots . The default duration is initially set to 4. Volume: Vn (n = 1-255) The V command sets the current volume. Larger is louder. The volume is initially set to 100. As an amateur composer, Dick decided to play his pieces of music by the PLAY statement. He managed to write a program with a long MML sequence, and attempted to run the program to play his music -- but unfortunately he encountered an unexpected error: the MML sequence was too long to be handled in his computer's small memory! Since he didn't want to give up all the efforts he had made to use the PLAY statement, he decided immediately to make the MML sequence shorter so that it fits in the small memory. It was too hard for him, though. So he asked you to write a program that, for each given MML sequence, prints the shortest MML sequence (i.e. MML sequence containing minimum number of characters) that expresses the same music as the given one. Note that the final values of octave, volume, and default duration can be differrent from the original MML sequence. Input The input consists of multiple data sets. Each data set is given by a single line that contains an MML sequence up to 100,000 characters. All sequences only contain the commands described above. Note that each sequence contains at least one note, and there is no rest before the first note and after the last note. The end of input is indicated by a line that only contains "". This is not part of any data sets and hence should not be processed. Output For each test case, print its case number and the shortest MML sequence on a line. If there are multiple solutions, print any of them. Sample Input C4C4G4G4A4A4G2F4F4E4E4D4D4C2 O4C4.C8F4.F8G8F8E8D8C2 B-8>C8<B-8V40R2R..R8.V100EV50L1CG Output for the Sample Input Case 1: CCGGAAG2FFEEDDC2 Case 2: C.C8F.L8FGFEDC2 Case 3: L8B-B+B-RL1RE4V50CG	36,163
Problem C: Pollock's conjecture The n th triangular number is defined as the sum of the first n positive integers. The n th tetrahedral number is defined as the sum of the first n triangular numbers. It is easy to show that the n th tetrahedral number is equal to n ( n +1)( n +2) ⁄ 6. For example, the 5th tetrahedral number is 1+(1+2)+(1+2+3)+(1+2+3+4)+(1+2+3+4+5) = 5×6×7 ⁄ 6 = 35. The first 5 triangular numbers 1, 3, 6, 10, 15 The first 5 tetrahedral numbers 1, 4, 10, 20, 35 In 1850, Sir Frederick Pollock, 1st Baronet, who was not a professional mathematician but a British lawyer and Tory (currently known as Conservative) politician, conjectured that every positive integer can be represented as the sum of at most five tetrahedral numbers. Here, a tetrahedral number may occur in the sum more than once and, in such a case, each occurrence is counted separately. The conjecture has been open for more than one and a half century. Your mission is to write a program to verify Pollock's conjecture for individual integers. Your program should make a calculation of the least number of tetrahedral numbers to represent each input integer as their sum. In addition, for some unknown reason, your program should make a similar calculation with only odd tetrahedral numbers available. For example, one can represent 40 as the sum of 2 tetrahedral numbers, 4×5×6 ⁄ 6 + 4×5×6 ⁄ 6, but 40 itself is not a tetrahedral number. One can represent 40 as the sum of 6 odd tetrahedral numbers, 5×6×7 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6 + 1×2×3 ⁄ 6, but cannot represent as the sum of fewer odd tetrahedral numbers. Thus, your program should report 2 and 6 if 40 is given. Input The input is a sequence of lines each of which contains a single positive integer less than 10 6 . The end of the input is indicated by a line containing a single zero. Output For each input positive integer, output a line containing two integers separated by a space. The first integer should be the least number of tetrahedral numbers to represent the input integer as their sum. The second integer should be the least number of odd tetrahedral numbers to represent the input integer as their sum. No extra characters should appear in the output. Sample Input 40 14 5 165 120 103 106 139 0 Output for the Sample Input 2 6 2 14 2 5 1 1 1 18 5 35 4 4 3 37	36,164
Score: 500 points Problem Statement In the Kingdom of AtCoder, only banknotes are used as currency. There are 10^{100}+1 kinds of banknotes, with the values of 1, 10, 10^2, 10^3, \dots, 10^{(10^{100})} . You have come shopping at a mall and are now buying a takoyaki machine with a value of N . (Takoyaki is the name of a Japanese snack.) To make the payment, you will choose some amount of money which is at least N and give it to the clerk. Then, the clerk gives you back the change, which is the amount of money you give minus N . What will be the minimum possible number of total banknotes used by you and the clerk, when both choose the combination of banknotes to minimize this count? Assume that you have sufficient numbers of banknotes, and so does the clerk. Constraints N is an integer between 1 and 10^{1,000,000} (inclusive). Input Input is given from Standard Input in the following format: N Output Print the minimum possible number of total banknotes used by you and the clerk. Sample Input 1 36 Sample Output 1 8 If you give four banknotes of value 10 each, and the clerk gives you back four banknotes of value 1 each, a total of eight banknotes are used. The payment cannot be made with less than eight banknotes in total, so the answer is 8 . Sample Input 2 91 Sample Output 2 3 If you give two banknotes of value 100, 1 , and the clerk gives you back one banknote of value 10 , a total of three banknotes are used. Sample Input 3 314159265358979323846264338327950288419716939937551058209749445923078164062862089986280348253421170 Sample Output 3 243	36,165
Score : 1000 points Problem Statement Takahashi and Aoki are going to together construct a sequence of integers. First, Takahashi will provide a sequence of integers a , satisfying all of the following conditions: The length of a is N . Each element in a is an integer between 1 and K , inclusive. a is a palindrome , that is, reversing the order of elements in a will result in the same sequence as the original. Then, Aoki will perform the following operation an arbitrary number of times: Move the first element in a to the end of a . How many sequences a can be obtained after this procedure, modulo 10^9+7 ? Constraints 1≤N≤10^9 1≤K≤10^9 Input The input is given from Standard Input in the following format: N K Output Print the number of the sequences a that can be obtained after the procedure, modulo 10^9+7 . Sample Input 1 4 2 Sample Output 1 6 The following six sequences can be obtained: (1, 1, 1, 1) (1, 1, 2, 2) (1, 2, 2, 1) (2, 2, 1, 1) (2, 1, 1, 2) (2, 2, 2, 2) Sample Input 2 1 10 Sample Output 2 10 Sample Input 3 6 3 Sample Output 3 75 Sample Input 4 1000000000 1000000000 Sample Output 4 875699961	36,166
ヒバラ海に沈む遺跡アイヅ考古学会は、ヒバラ海に沈む古代国家イワシロの遺跡調査に乗り出した。遺跡はヒバラ海のどこか一か所に存在する。そこで、探査レーダを使い、海岸線からのレーダ探査で遺跡の位置のおおよその目星を付け、海岸線から最大何メートル離れた位置まで調査しなければならないかを見積もることにした。上図のような直線で表された海岸線上に観測点を設置し、探査レーダを置く。探査レーダでは、観測点を中心とする、ある大きさの半円の範囲に遺跡があるということしかわからない。しかし、複数の観測データを組み合わせることで、より狭い範囲に絞り込むことができる。観測点の位置と探査レーダが示す半径からなるいくつかの観測データが与えられたとき、海岸線から最大でどのくらいの距離まで調査する必要があるかを求めるプログラムを作成せよ。 Input 入力は以下の形式で与えられる。 N x 1 r 1 x 2 r 2 : x N r N １行目に探査レーダによって測定されたデータの数 N (1 ≤ N ≤ 100000) が与えられる。続く N 行に、観測データ i の海岸線上での位置をメートル単位で表す整数 x i (0 ≤ x i ≤ 1,000,000) と、その位置から半径何メートル以内に遺跡が存在するかを表す整数 r i (1 ≤ r i ≤ 1,000,000) が与えられる。観測点が同じ観測データが２つ以上与えられることもある。与えられた観測データが複数の場合、それらすべての半円に含まれる点が必ず存在すると考えてよい。 Output 海岸線から最大で何メートルまで調査する必要があるかを実数で出力する。ただし、誤差がプラスマイナス 0.001 メートルを超えてはならない。この条件を満たせば小数点以下は何桁表示してもよい。 Sample Input 1 2 0 2 1 2 Sample Output 1 1.936 Sample Input 2 3 0 3 1 2 2 1 Sample Output 2 1.0 Sample Input 3 2 0 1 3 2 Sample Output 3 0.0	36,167
Bitonic Traveling Salesman Problem (Bitonic TSP) For given $N$ points in the 2D Euclidean plane, find the distance of the shortest tour that meets the following criteria: Visit the points according to the following steps: It starts from the leftmost point (starting point), goes strictly from left to right, and then visits the rightmost point (turn-around point). Then it starts from the turn-around point, goes strictly from right to left, and then back to the starting point. Through the processes 1. 2., the tour must visit each point at least once. Input The input data is given in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ ... $x_N$ $y_N$ Constraints $2 \leq N \leq 1000$ $-1000 \leq x_i, y_i \leq 1000$ $x_i$ differ from each other The given points are already sorted by x-coordinates Output Print the distance of the shortest tour in a line. The output should not have an error greater than 0.0001. Sample Input 1 3 0 0 1 1 2 0 Sample Output 1 4.82842712 Sample Input 2 4 0 1 1 2 2 0 3 1 Sample Output 2 7.30056308 Sample Input 3 5 0 0 1 2 2 1 3 2 4 0 Sample Output 3 10.94427191	36,168
カードの並び替え問題 1 から 2n の数が書かれた 2n 枚のカードがあり，上から 1, 2, 3, ... , 2n の順に積み重なっている．このカードを，次の方法を何回か用いて並べ替える．整数 k でカット上から k 枚のカードの山 A と残りのカードの山 B に分けた後，山 A の上に山 B をのせる．リフルシャッフル上から n 枚の山 A と残りの山 B に分け，上から A の1枚目， B の1枚目， A の2枚目， B の2枚目， …， A の n枚目， B の n枚目，となるようにして， 1 つの山にする．入力の指示に従い，カードを並び替えたあとのカードの番号を，上から順番に出力するプログラムを作成せよ．入力 1 行目には n （1 ≦ n ≦ 100）が書かれている．すなわちカードの枚数は 2n 枚である． 2 行目には操作の回数 m （1 ≦ m ≦ 1000）が書かれている． 3 行目から m + 2 行目までの m 行には， 0 から 2n-1 までのいずれか 1 つの整数 k が書かれており，カードを並べ替える方法を順に指定している． k = 0 の場合は，リフルシャッフルを行う． 1 ≦ k ≦ 2n-1 の場合は， k でカットを行う．出力出力は2n 行からなる． 1 行目には並べ替え終了後の一番上のカードの番号， 2 行目には並べ替え終了後の上から 2 番目のカードの番号というように， i 行目には上から i 番目のカードの番号を出力せよ．入出力例入力例 1 2 2 1 0 出力例 1 2 4 3 1 入力例 2 3 4 2 4 0 0 出力例 2 1 5 4 3 2 6 上記問題文と自動審判に使われるデータは、情報オリンピック日本委員会が作成し公開している問題文と採点用テストデータです。	36,169
三目並べ三目並べは，３ × ３のマス目の中に交互に ○ と × を入れていき、縦・横・斜めの何れかに一列 ○ か × が並んだときに、勝ちとなるゲームです（図1〜図3 を参照）図１：○の勝ち図２：× の勝ち図３：引き分け三目並べは、○と×が交互にマス目を埋めていき、どちらかが一列揃ったときにゲーム終了となります。そのため、図 4 のように、○と×が両方とも一列そろっている場合はありえない局面です。ありえない局面が入力されることはありません。図４：ありえない局面三目並べの盤面を読み込んで、勝敗の結果を出力するプログラムを作成して下さい。 Input 入力は複数のデータセットからなります。各データセットとして、盤面を表す１つの文字列が１行に与えられます。盤面の文字列は、○、×、空白をそれぞれ半角英小文字の o、x、s であらわし、下図のマス目の順に並んでいます。データセットの数は 50 を超えません。 Output データセットごとに、○が勝ちなら半角英小文字の o を、×が勝ちなら半角英小文字の x を、引き分けならば半角英小文字の d を１行に出力してください。 Sample Input ooosxssxs xoosxsosx ooxxxooxo Output for the Sample Input o x d	36,170
Score : 200 points Problem Statement Evi has N integers a_1,a_2,..,a_N . His objective is to have N equal integers by transforming some of them. He may transform each integer at most once. Transforming an integer x into another integer y costs him (x-y)^2 dollars. Even if a_i=a_j (i≠j) , he has to pay the cost separately for transforming each of them (See Sample 2). Find the minimum total cost to achieve his objective. Constraints 1≦N≦100 -100≦a_i≦100 Input The input is given from Standard Input in the following format: N a_1 a_2 ... a_N Output Print the minimum total cost to achieve Evi's objective. Sample Input 1 2 4 8 Sample Output 1 8 Transforming the both into 6 s will cost (4-6)^2+(8-6)^2=8 dollars, which is the minimum. Sample Input 2 3 1 1 3 Sample Output 2 3 Transforming the all into 2 s will cost (1-2)^2+(1-2)^2+(3-2)^2=3 dollars. Note that Evi has to pay (1-2)^2 dollar separately for transforming each of the two 1 s. Sample Input 3 3 4 2 5 Sample Output 3 5 Leaving the 4 as it is and transforming the 2 and the 5 into 4 s will achieve the total cost of (2-4)^2+(5-4)^2=5 dollars, which is the minimum. Sample Input 4 4 -100 -100 -100 -100 Sample Output 4 0 Without transforming anything, Evi's objective is already achieved. Thus, the necessary cost is 0 .	36,171
Problem E: カントリーロードある過疎地域での話である．この地域ではカントリーロードと呼ばれるまっすぐな道に沿って，家がまばらに建っている．今までこの地域には電気が通っていなかったのだが，今回政府からいくつかの発電機が与えられることになった．発電機は好きなところに設置できるが，家に電気が供給されるにはどれかの発電機に電線を介してつながっていなければならず，電線には長さに比例するコストが発生する．地域で唯一の技術系公務員であるあなたの仕事は，すべての家に電気が供給されるという条件の下で，できるだけ電線の長さの総計が短くなるような発電機および電線の配置を求めることである．なお，発電機の容量は十分に大きいので，いくらでも多くの家に電気を供給することができるものとする．サンプル入力の1番目のデータセットを図2に示す．この問題に対する最適な配置を与えるには，図のように x = 20 と x = 80 の位置に発電機を配置し，それぞれ図中のグレーで示した位置に電線を引けばよい．図2: 発電機と電線の配置の例（入力例の最初のデータセット）． Input 入力の1行目にはデータセットの個数 t (0 < t ≤ 50) が与えられる．引き続き t 個のデータセットが与えられる．データセットはそれぞれ次のような形式で2行で与えられる． n k x 1 x 2 ... x n n は家の戸数， k は発電機の個数である． x 1 , x 2 , ..., x n はそれぞれ家の位置を表す一次元座標である．これらの値はすべて整数であり， 0 < n ≤ 100000, 0 < k ≤ 100000, 0 ≤ x 1 < x 2 < ... < x n ≤ 1000000 を満たす．さらに，データセットのうち 90% は， 0 < n ≤ 100, 0 < k ≤ 100 を満たしている． Output 各データセットに対し，必要な電線の長さの総計の最小値を1行に出力せよ． Sample Input 6 5 2 10 30 40 70 100 7 3 3 6 10 17 21 26 28 1 1 100 2 1 0 1000000 3 5 30 70 150 6 4 0 10 20 30 40 50 Output for the Sample Input 60 13 0 1000000 0 20	36,172
Score : 200 points Problem Statement We have a sequence p = { p_1,\ p_2,\ ...,\ p_N } which is a permutation of { 1,\ 2,\ ...,\ N }. You can perform the following operation at most once: choose integers i and j (1 \leq i < j \leq N) , and swap p_i and p_j . Note that you can also choose not to perform it. Print YES if you can sort p in ascending order in this way, and NO otherwise. Constraints All values in input are integers. 2 \leq N \leq 50 p is a permutation of { 1,\ 2,\ ...,\ N }. Input Input is given from Standard Input in the following format: N p_1 p_2 ... p_N Output Print YES if you can sort p in ascending order in the way stated in the problem statement, and NO otherwise. Sample Input 1 5 5 2 3 4 1 Sample Output 1 YES You can sort p in ascending order by swapping p_1 and p_5 . Sample Input 2 5 2 4 3 5 1 Sample Output 2 NO In this case, swapping any two elements does not sort p in ascending order. Sample Input 3 7 1 2 3 4 5 6 7 Sample Output 3 YES p is already sorted in ascending order, so no operation is needed.	36,173
Problem I Starting a Scenic Railroad Service Jim, working for a railroad company, is responsible for planning a new tourist train service. He is sure that the train route along a scenic valley will arise a big boom, but not quite sure how big the boom will be. A market survey was ordered and Jim has just received an estimated list of passengers' travel sections. Based on the list, he'd like to estimate the minimum number of train seats that meets the demand. Providing as many seats as all of the passengers may cost unreasonably high. Assigning the same seat to more than one passenger without overlapping travel sections may lead to a great cost cutback. Two different policies are considered on seat assignments. As the views from the train windows depend on the seat positions, it would be better if passengers can choose a seat. One possible policy (named `policy-1') is to allow the passengers to choose an arbitrary seat among all the remaining seats when they make their reservations. As the order of reservations is unknown, all the possible orders must be considered on counting the required number of seats. The other policy (named `policy-2') does not allow the passengers to choose their seats; the seat assignments are decided by the railroad operator, not by the passengers, after all the reservations are completed. This policy may reduce the number of the required seats considerably. Your task is to let Jim know how di erent these two policies are by providing him a program that computes the numbers of seats required under the two seat reservation policies. Let us consider a case where there are four stations, S1, S2, S3, and S4, and four expected passengers $p_1$, $p_2$, $p_3$, and $p_4$ with the travel list below. passenger from to $p_1$ S1 S2 $p_2$ S2 S3 $p_3$ S1 S3 $p_4$ S3 S4 The travel sections of $p_1$ and $p_2$ do not overlap, that of $p_3$ overlaps those of $p_1$ and $p_2$, and that of $p_4$ does not overlap those of any others. Let's check if two seats would suffice under the policy-1. If $p_1$ books a seat first, either of the two seats can be chosen. If $p_2$ books second, as the travel section does not overlap that of $p_1$, the same seat can be booked, but the other seat may look more attractive to $p_2$. If $p_2$ reserves a seat different from that of $p_1$, there will remain no available seats for $p_3$ between S1 and S3 (Figure I.1). Figure I.1. With two seats With three seats, $p_3$ can find a seat with any seat reservation combinations by $p_1$ and $p_2$. $p_4$ can also book a seat for there are no other passengers between S3 and S4 (Figure I.2). Figure I.2. With three seats For this travel list, only three seats suffice considering all the possible reservation orders and seat preferences under the policy-1. On the other hand, deciding the seat assignments after all the reservations are completed enables a tight assignment with only two seats under the policy-2 (Figure I.3). Figure I.3. Tight assignment to two seats Input The input consists of a single test case of the following format. $n$ $a_1$ $b_1$ ... $a_n$ $b_n$ Here, the first line has an integer $n$, the number of the passengers in the estimated list of passengers' travel sections ($1 \leq n \leq 200 000$). The stations are numbered starting from 1 in their order along the route. Each of the following $n$ lines describes the travel for each passenger by two integers, the boarding and the alighting station numbers, $a_i$ and $b_i$, respectively ($1 \leq a_i < b_i \leq 100 000$). Note that more than one passenger in the list may have the same boarding and alighting stations. Output Two integers $s_1$ and $s_2$ should be output in a line in this order, separated by a space. $s_1$ and $s_2$ are the numbers of seats required under the policy-1 and -2, respectively. Sample Input 1 4 1 3 1 3 3 6 3 6 Sample Output 1 2 2 Sample Input 2 4 1 2 2 3 1 3 3 4 Sample Output 2 3 2 Sample Input 3 10 84 302 275 327 364 538 26 364 29 386 545 955 715 965 404 415 903 942 150 402 Sample Output 3 6 5	36,174
Problem Statement Nathan O. Davis is a student at the department of integrated systems. Today's agenda in the class is audio signal processing. Nathan was given a lot of homework out. One of the homework was to write a program to process an audio signal. He copied the given audio signal to his USB memory and brought it back to his home. When he started his homework, he unfortunately dropped the USB memory to the floor. He checked the contents of the USB memory and found that the audio signal data got broken. There are several characteristics in the audio signal that he copied. The audio signal is a sequence of $N$ samples. Each sample in the audio signal is numbered from $1$ to $N$ and represented as an integer value. Each value of the odd-numbered sample(s) is strictly smaller than the value(s) of its neighboring sample(s). Each value of the even-numbered sample(s) is strictly larger than the value(s) of its neighboring sample(s). He got into a panic and asked you for a help. You tried to recover the audio signal from his USB memory but some samples of the audio signal are broken and could not be recovered. Fortunately, you found from the metadata that all the broken samples have the same integer value. Your task is to write a program, which takes the broken audio signal extracted from his USB memory as its input, to detect whether the audio signal can be recovered uniquely. Input The input consists of multiple datasets. The form of each dataset is described below. $N$ $a_{1}$ $a_{2}$ ... $a_{N}$ The first line of each dataset consists of an integer, $N (2 \le N \le 1{,}000)$. $N$ denotes the number of samples in the given audio signal. The second line of each dataset consists of $N$ values separated by spaces. The $i$-th value, $a_{i}$, is either a character x or an integer between $-10^9$ and $10^9$, inclusive. It represents the $i$-th sample of the broken audio signal. If $a_{i}$ is a character x , it denotes that $i$-th sample in the audio signal is broken. Otherwise it denotes the value of the $i$-th sample. The end of input is indicated by a single $0$. This is not included in the datasets. You may assume that the number of the datasets does not exceed $100$. Output For each dataset, output the value of the broken samples in one line if the original audio signal can be recovered uniquely. If there are multiple possible values, output ambiguous . If there are no possible values, output none . Sample Input 5 1 x 2 4 x 2 x x 2 1 2 2 2 1 2 1000000000 x 4 x 2 1 x 0 Output for the Sample Input 3 none ambiguous none ambiguous none	36,175
Problem D: Dice Room You are playing a popular video game which is famous for its depthful story and interesting puzzles. In the game you were locked in a mysterious house alone and there is no way to call for help, so you have to escape on yours own. However, almost every room in the house has some kind of puzzles and you cannot move to neighboring room without solving them. One of the puzzles you encountered in the house is following. In a room, there was a device which looked just like a dice and laid on a table in the center of the room. Direction was written on the wall. It read: "This cube is a remote controller and you can manipulate a remote room, Dice Room, by it. The room has also a cubic shape whose surfaces are made up of 3x3 unit squares and some squares have a hole on them large enough for you to go though it. You can rotate this cube so that in the middle of rotation at least one edge always touch the table, that is, to 4 directions. Rotating this cube affects the remote room in the same way and positions of holes on the room change. To get through the room, you should have holes on at least one of lower three squares on the front and back side of the room." You can see current positions of holes by a monitor. Before going to Dice Room, you should rotate the cube so that you can go though the room. But you know rotating a room takes some time and you don’t have much time, so you should minimize the number of rotation. How many rotations do you need to make it possible to get though Dice Room? Input The input consists of several datasets. Each dataset contains 6 tables of 3x3 characters which describe the initial position of holes on each side. Each character is either ' * ' or ' . '. A hole is indicated by ' * '. The order which six sides appears in is: front, right, back, left, top, bottom. The order and orientation of them are described by this development view: Figure 4: Dice Room Figure 5: available dice rotations There is a blank line after each dataset. The end of the input is indicated by a single ' # '. Output Print the minimum number of rotations needed in a line for each dataset. You may assume all datasets have a solution. Sample Input ... ... .. ... ... .. ... ... ... ... ... .. ... ... .. ... ... ... ... .. ... .. ... ..* . . . . .. .* .. .. ..* . ... . ... .. .. ... .** .. ... ... .. .. ... .. ..* ... .** ... *.. ... # Output for the Sample Input 3 1 0	36,176
流れ星に願いを謎の組織 JAG (Japanese Alumni Group) では定期的に会議を開いている．ある日の議題は「近日行われる ICPC (International Collegiate Programming Contest) 国内予選で参加チームが力を発揮できるようにするには」であった．会議の結論として流れ星に各チームの健闘を祈ることになり，彼らは本部を置く建物の屋上に出た．彼らが屋上に出ると，空には $n$ 個の流れ星が見えていた．流れ星は3次元空間上の球として表され，$1$ から $n$ の番号が割り振られている．星に詳しいメンバーにより，各流れ星は一定の速度で直線的に移動すると同時に，一定の速度で半径が小さくなっていくとみなせることが分かった．実際に測定してみたところ，各流れ星の初期位置 $(px_i, py_i, pz_i)$，移動速度 $(vx_i, vy_i, vz_i)$，初期半径 $r_i$，消滅速度 $vr_i$ が分かった．これは流れ星 $i$ が時刻 $t$ ($t \geq 0$) で中心座標 $(px_i + t vx_i, py_i + t vy_i, pz_i + t vz_i)$，半径 $r_i - t vr_i$ の球となる事を表している．流れ星は，半径が 0 になった瞬間に自然消滅してしまう．また，2つの流れ星が接触した場合はどちらの流れ星も消滅してしまう．あなたの仕事は，効率よく参加チームの健闘を祈ることができるように，各流れ星が消滅するまでの時間を求めることである．彼らの中には卓越した視力の持ち主がいるため，情報が与えられた $n$ 個以外に流れ星が存在する可能性については考慮しなくても良い．加えて，彼らは非常に効率よく流れ星の観測を行ったため，観測にかかった時間は無視できるほど小さいと考えて良い． Input 入力は複数のデータセットから構成され，1つの入力に含まれるデータセットの数は100以下である．各データセットの形式は次の通りである． $n$ $px_1$ $py_1$ $pz_1$ $vx_1$ $vy_1$ $vz_1$ $r_1$ $vr_1$ ... $px_n$ $py_n$ $pz_n$ $vx_n$ $vy_n$ $vz_n$ $r_n$ $vr_n$ $n$ は流れ星の数を表す整数であり，$1$ 以上 $200$ 以下と仮定して良い．続く $n$ 行には流れ星の情報が与えられる．各行は小数点以下4桁で表される8つの値を含み，$(px_i, py_i, pz_i)$ は流れ星 $i$ の初期位置を，$(vx_i, vy_i, vz_i)$ は移動速度を，$r_i$ は初期半径を，$vr_i$ は消滅速度をそれぞれ表す．与えられる値について，$-1{,}000 \leq px_i \leq 1{,}000$，$-1{,}000 \leq py_i \leq 1{,}000$，$-1{,}000 \leq pz_i \leq 1{,}000$，$-100 \leq vx_i \leq 100$， $-100 \leq vy_i \leq 100$， $-100 \leq vz_i \leq 100$，$1 \leq r_i \leq 100$，$1 \leq vr_i \leq 100$ であると仮定して良い．また，与えられるデータセットについて以下を仮定して良い．ある1つの流れ星の初期半径が $10^{-8}$ 変化しても，接触する星のペアの集合は変わらないある1つの流れ星が接触により消滅しないと仮定しても，$10^{-8}$ 以内の時間で2つ以上の流れ星に接触したり，他の流れ星と接触する時刻から$10^{-8}$以内に自然消滅することはない初期状態ではどの2つの流れ星も重なっておらず，$10^{-8}$以上の距離を空けている時刻 $t < 10^{-8}$ ではどの2つの流れ星も接触しない $n = 0$ は入力の終わりを示す．これはデータセットには含めない． Output 各データセットについて，各流れ星が消滅するまでの時間を流れ星1から順にそれぞれ1行に出力しなさい．出力には$10^{-8}$を超える絶対誤差があってはならない．それ以外の余計な文字を出力してはならない． Sample Input 1 0.0000 0.0000 0.0000 2.0000 0.0000 0.0000 4.0000 1.0000 2 0.0000 0.0000 0.0000 2.0000 0.0000 0.0000 4.0000 1.0000 10.0000 0.0000 0.0000 -2.0000 0.0000 0.0000 4.0000 1.0000 5 -10.0000 0.0000 0.0000 10.0000 0.0000 0.0000 2.0000 1.0000 -5.0000 0.0000 0.0000 10.0000 0.0000 0.0000 2.0000 1.0000 0.0000 0.0000 0.0000 10.0000 0.0000 0.0000 2.0000 1.0000 11.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1.0000 100.0000 15.0000 0.0000 0.0000 -10.0000 0.0000 0.0000 2.0000 1.0000 27 -45.6243 -40.4815 42.0513 -0.8380 -6.3628 4.5484 12.0279 2.2721 8.7056 -9.8256 34.1560 6.0068 6.2527 -6.8506 28.9807 1.5037 30.1481 29.9591 -46.2881 6.7611 8.6669 1.5629 14.5578 1.3181 24.2927 8.3779 -21.8931 0.7074 0.1879 -8.9742 5.5877 2.6893 25.3009 -42.9168 10.7480 -7.2477 -8.5507 7.7846 13.7923 2.8726 17.6938 42.3577 -5.0334 6.4949 -2.1472 -5.3101 23.3066 1.4769 -7.9296 -29.6442 -24.2157 -1.1064 -9.5802 6.5858 12.4250 2.3816 9.5851 -20.0455 -35.1885 5.7477 -1.0622 2.5211 3.5233 1.2466 -35.5762 44.5412 -46.7816 3.6053 0.4991 4.3470 20.6922 2.8529 -44.9386 -48.0381 -43.6877 7.4101 3.9491 7.1619 10.4301 2.4920 -49.9870 -28.6276 -2.6522 5.8008 -1.0054 -4.9061 25.1188 1.4916 45.0228 31.3811 29.2546 -8.7777 -3.7836 -7.7180 17.4361 1.8706 35.5553 45.8774 -29.8025 -7.3596 -9.2114 -3.5987 6.8841 2.6143 19.9857 34.3874 42.5551 5.2133 -5.5350 -7.6617 2.9294 1.4026 23.5109 18.1633 -34.8265 7.3260 -4.1912 5.3518 3.0036 1.5027 43.5134 -27.5238 49.4679 -4.5986 1.8410 6.8741 2.2009 1.4525 -28.8994 23.2934 -6.1914 5.7985 -6.2129 -8.2882 16.1683 1.7463 3.6721 38.2528 -38.7741 4.5115 6.6442 6.4406 10.7555 1.0971 17.4488 -12.6965 -23.1293 2.8257 6.3319 -1.5368 7.3785 2.9350 33.2708 -17.9437 -0.5347 8.7428 7.3193 5.9738 6.2292 2.6210 -14.4660 -25.1449 -4.4191 -9.4843 -6.6439 -4.7330 7.7910 2.1659 32.4428 -24.2605 48.1228 -5.2396 1.5916 -5.9552 1.1760 1.3618 -21.9088 43.6286 -8.8286 6.4641 0.5554 -4.6827 1.2504 1.4718 -0.1784 -42.1729 -2.7193 5.3741 0.9098 9.7622 1.4764 1.2611 29.3245 -33.2298 -26.3824 -8.4192 -2.9427 -7.3759 9.6346 1.7490 -35.1767 35.9652 33.4779 4.0088 2.4579 2.0981 19.2565 1.7121 -17.5530 1.4161 -14.0271 6.4564 -4.8261 -8.7461 3.0566 1.5906 0 Output for Sample Input 4.0000000000 1.0000000000 1.0000000000 2.0000000000 2.0000000000 0.6111111111 0.0100000000 0.6111111111 5.2937370714 0.3931996496 11.0445337986 2.0777525750 4.8013298058 0.0925901184 5.2170809540 2.8263276111 7.2530407655 4.1854333868 0.2348376111 1.0517364512 0.0925901184 1.0517364512 1.9988021561 1.5152495697 9.2586039054 9.8035730562 2.5139693356 2.3766501335 0.2348376111 0.3931996496 0.8495719527 1.1707239711 5.5086335049 11.2472986391 1.9216647806	36,177
Problem B: Lagrange's Four-Square Theorem The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are. For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 4 2 + 3 2 and 3 2 + 4 2 are the same representation. For example, let’s check the case of 25. This integer has just three representations 1 2 +2 2 +2 2 +4 2 , 3 2 + 4 2 , and 5 2 . Thus you should report 3 in this case. Be careful not to count 4 2 + 3 2 and 3 2 + 4 2 separately. Input The input is composed of at most 255 lines, each containing a single positive integer less than 2 15 , followed by a line containing a single zero. The last line is not a part of the input data. Output The output should be composed of lines, each containing a single integer. No other characters should appear in the output. The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares. Sample Input 1 25 2003 211 20007 0 Output for the Sample Input 1 3 48 7 738	36,178
Nathan O. Davis is running a company. His company owns a web service which has a lot of users. So his office is full of servers, routers and messy LAN cables. He is now very puzzling over the messy cables, because they are causing many kinds of problems. For example, staff working at the company often trip over a cable. No damage if the cable is disconnected. It's just lucky. Computers may fall down and get broken if the cable is connected. He is about to introduce a new computer and a new cable. He wants to minimize staff's steps over the new cable. His office is laid-out in a two-dimensional grid with H \times W cells. The new cable should weave along edges of the cells. Each end of the cable is at a corner of a cell. The grid is expressed in zero-origin coordinates, where the upper left corner is (0, 0). Each staff starts his/her work from inside a certain cell and walks in the office along the grid in a fixed repeated pattern every day. A walking pattern is described by a string of four characters U , D , L and R . U means moving up, D means moving down, R means moving to the right, and L means moving to the left. For example, UULLDDRR means moving up, up, left, left, down, down, right and right in order. The staff repeats the pattern fixed T times. Note that the staff stays in the cell if the staff is going out of the grid through the wall. You have the moving patterns of all staff and the positions of both ends of the new cable. Your job is to find an optimal placement of the new cable, which minimizes the total number his staff would step over the cable. Input The first line of the input contains three integers which represent the dimension of the office W , H ( 1 \leq W, H \leq 500 ), and the number of staff N ( 1 \leq N \leq 1000 ), respectively. The next line contains two x-y pairs ( 0 \leq x \leq W , 0 \leq y \leq H ), which mean the position of two endpoints of a LAN cable to be connected. These values represents the coordinates of the cells to which the cable is plugged in its top-left corner. Exceptionally, x = W means the right edge of the rightmost cell, and y = H means the bottom edge of the bottommost cell. Following lines describe staff's initial positions and their moving patterns. The first line includes an x - y pair ( 0 \leq x \lt W , 0 \leq y \lt H ), which represents the coordinate of a staff's initial cell. The next line has an integer T ( 1 \leq T \leq 100 ) and a string which consists of U , D , L and R , whose meaning is described as above. The length of a pattern string is greater than or equal to 1 , and no more than 1,000 . These two lines are repeated N times. Output Output the minimum number of times his staff step over the cable in a single line. Sample Input 1 3 3 1 1 1 3 3 0 0 1 RRDDLLUU Output for the Sample Input 1 1 Sample Input 2 3 3 1 0 0 3 3 0 0 1 RRDDLLUU Output for the Sample Input 2 0 Sample Input 3 3 3 1 1 1 3 3 0 0 10 RRDDLLUU Output for the Sample Input 3 10 Sample Input 4 3 3 4 1 1 3 3 0 0 10 R 2 0 10 D 2 2 10 L 0 2 10 U Output for the Sample Input 4 1	36,179
定期券(Commuter Pass) JOI 君が住む都市には N 個の駅があり，それぞれ 1, 2, ..., N の番号が付けられている．また， M 本の鉄道路線があり，それぞれ 1, 2, ..., M の番号が付けられている．鉄道路線 i ( 1 \leq i \leq M ) は駅 A_i と駅 B_i を双方向に結んでおり，乗車運賃は C_i 円である． JOI 君は駅S の近くに住んでおり，駅 T の近くのIOI 高校に通っている．そのため，両者を結ぶ定期券を購入することにした．定期券を購入する際には，駅 S と駅 T の間を最小の運賃で移動する経路を一つ指定しなければならない．この定期券を用いると，指定した経路に含まれる鉄道路線は双方向に自由に乗り降りできる． JOI 君は，駅 U および駅 V の近くにある書店もよく利用している．そこで，駅 U から駅 V への移動にかかる運賃ができるだけ小さくなるように定期券を購入したいと考えた．駅 U から駅 V への移動の際は，まず駅 U から駅 V への経路を1 つ選ぶ．この経路に含まれる鉄道路線 i において支払うべき運賃は，鉄道路線 i が定期券を購入する際に指定した経路に含まれる場合，0 円鉄道路線 i が定期券を購入する際に指定した経路に含まれない場合， C_i 円となる．この運賃の合計が，駅 U から駅 V への移動にかかる運賃である．定期券を購入する際に指定する経路をうまく選んだときの，駅 U から駅 V への移動にかかる運賃の最小値を求めたい．課題定期券を購入する際に指定する経路をうまく選んだときの，駅 U から駅 V への移動にかかる運賃の最小値を求めるプログラムを作成せよ．入力標準入力から以下の入力を読み込め． 1 行目には，2 個の整数 N, M が書かれている．これらは，JOI 君が住む都市に N 個の駅と M 本の鉄道路線があることを表す． 2 行目には，2 個の整数 S, T が書かれている．これらは，JOI 君が駅 S から駅 T への定期券を購入することを表す． 3 行目には，2 個の整数 U, V が書かれている．これらは，JOI 君が駅 U から駅 V への移動にかかる運賃を最小化したいことを表す．続く M 行のうちの i 行目( 1 \leq i \leq M ) には，3 個の整数 A_i, B_i,C_i が書かれている．これらは，鉄道路線 i が駅 A_i と駅 B_i を双方向に結び，その運賃が C_i 円であることを表す．出力標準出力に，定期券を購入する際に駅 S から駅 T への経路をうまく指定したときの，駅 U から駅 V への移動にかかる運賃の最小値を1 行で出力せよ．制限すべての入力データは以下の条件を満たす． 2 \leq N \leq 100 000． 1 \leq M \leq 200 000． 1 \leq S \leq N． 1 \leq T \leq N． 1 \leq U \leq N． 1 \leq V \leq N． S ≠ T． U ≠ V． S ≠ U または T ≠ V．どの駅から他のどの駅へも1 本以上の鉄道路線を用いて到達できる． 1 \leq A_i < B_i \leq N (1 \leq i l\leq M)． 1 \leq i < j \leq M に対し， A_i ≠ A_j または B_i ≠ B_j． 1 \leq C_i \leq 1 000 000 000 (1 \leq i \leq M)．入出力例入力例1 6 6 1 6 1 4 1 2 1 2 3 1 3 5 1 2 4 3 4 5 2 5 6 1 出力例1 2 この入力例では，定期券を買う際に指定できる経路は駅1 → 駅2 → 駅3 → 駅5 → 駅6 という経路に限られる．駅1 から駅4 への移動にかかる運賃を最小化するには，駅1 → 駅2 → 駅3 → 駅5 → 駅4 という経路を選べばよい．この経路を選んだ場合，各鉄道路線において支払うべき運賃は，駅4 と駅5 を結ぶ鉄道路線5 においては，2 円．それ以外の鉄道路線においては，0 円．となるので，かかる運賃の合計は2 円となる．入力例2 6 5 1 2 3 6 1 2 1000000000 2 3 1000000000 3 4 1000000000 4 5 1000000000 5 6 1000000000 出力例2 3000000000 この入力例では，駅3 から駅6 への移動に定期券を用いない．入力例3 8 8 5 7 6 8 1 2 2 2 3 3 3 4 4 1 4 1 1 5 5 2 6 6 3 7 7 4 8 8 出力例3 15 入力例4 5 5 1 5 2 3 1 2 1 2 3 10 2 4 10 3 5 10 4 5 10 出力例4 0 入力例5 10 15 6 8 7 9 2 7 12 8 10 17 1 3 1 3 8 14 5 7 15 2 3 7 1 10 14 3 6 12 1 5 10 8 9 1 2 9 7 1 4 1 1 8 1 2 4 7 5 6 16 出力例5 19 情報オリンピック日本委員会作『第17 回日本情報オリンピック(JOI 2017/2018) 本選』	36,180
最短経路図１に例示するように整数（0 以上 99 以下）をひしがたに並べます。このような、ひしがたを表すデータを読み込んで、一番上からスタートして一番下まで次のルールに従って進むとき、通過する整数の和の最大値を出力するプログラムを作成してください。各ステップで、対角線上の左下か対角線上の右下に進むことができます。例えば図1の例では、図2に示すように、7,3,8,7,5,7,8,3,7を選んで通ったとき、その和は最大の 55 （7+3+8+7+5+7+8+3+7=55）となります。 Input 入力例に示すように、カンマで区切られた整数の並びが、ひし形状に与えられます。各行に空白文字は含まれません。入力例は図１に対応しています。データの行数は 100 行未満です。 Output ルールに従って通過する整数の和の最大値を１行に出力します。 Sample Input 7 3,8 8,1,0 2,7,4,4 4,5,2,6,5 2,7,4,4 8,1,0 3,8 7 Sample Output 55	36,181
スピードスケートバッジテストスピードスケートバッジテストでは、2 種類の距離で規定されたタイムを上回った場合に級が認定されます。例えば A 級になるには 500 M で 40.0 秒未満、かつ 1000 M で 1 分 23 秒未満であることが求められます。スピードスケート大会 (500 M と 1000 M) で記録したタイムを入力とし、スピードスケートバッジテストで何級に相当するかを出力するプログラムを作成して下さい。500 M と1000 M のバッジテスト規定タイムは下表のとおりです。 E 級に満たなかった場合には、NA と出力してください。 500 M 1000 M AAA 級 35 秒 50 1 分 11 秒 00 AA 級 37 秒 50 1 分 17 秒 00 A 級 40 秒 00 1 分 23 秒 00 B 級 43 秒 00 1 分 29 秒 00 C 級 50 秒 00 1 分 45 秒 00 D 級 55 秒 00 1 分 56 秒 00 E 級 1分10 秒 00 2 分 28 秒 00 Input 複数のデータセットが与えられます。各データセットとして、500 M タイムと 1000 M タイムをそれぞれ表す実数 t 1 , t 2 (8.0 ≤ t 1 , t 2 ≤ 360.0) が空白区切りで与えられます。 t 1 , t 2 は秒単位で小数点以下最大 2 桁までの数字を含む実数で与えられます。データセットの数は 100 を超えません。 Output 各データセットごとに、判定結果 AAA ~ E または NA を１行に出力してください。 Sample Input 40.0 70.0 72.5 140.51 Output for the Sample Input B NA	36,182
Score : 400 points Problem Statement We have a grid with H rows and W columns. The square at the i -th row and the j -th column will be called Square (i,j) . The integers from 1 through H×W are written throughout the grid, and the integer written in Square (i,j) is A_{i,j} . You, a magical girl, can teleport a piece placed on Square (i,j) to Square (x,y) by consuming \|x-i\|+\|y-j\| magic points. You now have to take Q practical tests of your ability as a magical girl. The i -th test will be conducted as follows: Initially, a piece is placed on the square where the integer L_i is written. Let x be the integer written in the square occupied by the piece. Repeatedly move the piece to the square where the integer x+D is written, as long as x is not R_i . The test ends when x=R_i . Here, it is guaranteed that R_i-L_i is a multiple of D . For each test, find the sum of magic points consumed during that test. Constraints 1 \leq H,W \leq 300 1 \leq D \leq H×W 1 \leq A_{i,j} \leq H×W A_{i,j} \neq A_{x,y} ((i,j) \neq (x,y)) 1 \leq Q \leq 10^5 1 \leq L_i \leq R_i \leq H×W (R_i-L_i) is a multiple of D . Input Input is given from Standard Input in the following format: H W D A_{1,1} A_{1,2} ... A_{1,W} : A_{H,1} A_{H,2} ... A_{H,W} Q L_1 R_1 : L_Q R_Q Output For each test, print the sum of magic points consumed during that test. Output should be in the order the tests are conducted. Sample Input 1 3 3 2 1 4 3 2 5 7 8 9 6 1 4 8 Sample Output 1 5 4 is written in Square (1,2) . 6 is written in Square (3,3) . 8 is written in Square (3,1) . Thus, the sum of magic points consumed during the first test is (\|3-1\|+\|3-2\|)+(\|3-3\|+\|1-3\|)=5 . Sample Input 2 4 2 3 3 7 1 4 5 2 6 8 2 2 2 2 2 Sample Output 2 0 0 Note that there may be a test where the piece is not moved at all, and there may be multiple identical tests. Sample Input 3 5 5 4 13 25 7 15 17 16 22 20 2 9 14 11 12 1 19 10 6 23 8 18 3 21 5 24 4 3 13 13 2 10 13 13 Sample Output 3 0 5 0	36,183
Score: 200 points Problem Statement The restaurant AtCoder serves the following five dishes: ABC Don (rice bowl): takes A minutes to serve. ARC Curry: takes B minutes to serve. AGC Pasta: takes C minutes to serve. APC Ramen: takes D minutes to serve. ATC Hanbagu (hamburger patty): takes E minutes to serve. Here, the time to serve a dish is the time between when an order is placed and when the dish is delivered. This restaurant has the following rules on orders: An order can only be placed at a time that is a multiple of 10 (time 0 , 10 , 20 , ... ). Only one dish can be ordered at a time. No new order can be placed when an order is already placed and the dish is still not delivered, but a new order can be placed at the exact time when the dish is delivered. E869120 arrives at this restaurant at time 0 . He will order all five dishes. Find the earliest possible time for the last dish to be delivered. Here, he can order the dishes in any order he likes, and he can place an order already at time 0 . Constraints A, B, C, D and E are integers between 1 and 123 (inclusive). Input Input is given from Standard Input in the following format: A B C D E Output Print the earliest possible time for the last dish to be delivered, as an integer. Sample Input 1 29 20 7 35 120 Sample Output 1 215 If we decide to order the dishes in the order ABC Don, ARC Curry, AGC Pasta, ATC Hanbagu, APC Ramen, the earliest possible time for each order is as follows: Order ABC Don at time 0 , which will be delivered at time 29 . Order ARC Curry at time 30 , which will be delivered at time 50 . Order AGC Pasta at time 50 , which will be delivered at time 57 . Order ATC Hanbagu at time 60 , which will be delivered at time 180 . Order APC Ramen at time 180 , which will be delivered at time 215 . There is no way to order the dishes in which the last dish will be delivered earlier than this. Sample Input 2 101 86 119 108 57 Sample Output 2 481 If we decide to order the dishes in the order AGC Pasta, ARC Curry, ATC Hanbagu, APC Ramen, ABC Don, the earliest possible time for each order is as follows: Order AGC Pasta at time 0 , which will be delivered at time 119 . Order ARC Curry at time 120 , which will be delivered at time 206 . Order ATC Hanbagu at time 210 , which will be delivered at time 267 . Order APC Ramen at time 270 , which will be delivered at time 378 . Order ABC Don at time 380 , which will be delivered at time 481 . There is no way to order the dishes in which the last dish will be delivered earlier than this. Sample Input 3 123 123 123 123 123 Sample Output 3 643 This is the largest valid case.	36,184
Graph There are two standard ways to represent a graph $G = (V, E)$, where $V$ is a set of vertices and $E$ is a set of edges; Adjacency list representation and Adjacency matrix representation. An adjacency-list representation consists of an array $Adj[\|V\|]$ of $\|V\|$ lists, one for each vertex in $V$. For each $u \in V$, the adjacency list $Adj[u]$ contains all vertices $v$ such that there is an edge $(u, v) \in E$. That is, $Adj[u]$ consists of all vertices adjacent to $u$ in $G$. An adjacency-matrix representation consists of $\|V\| \times \|V\|$ matrix $A = a_{ij}$ such that $a_{ij} = 1$ if $(i, j) \in E$, $a_{ij} = 0$ otherwise. Write a program which reads a directed graph $G$ represented by the adjacency list, and prints its adjacency-matrix representation. $G$ consists of $n\; (=\|V\|)$ vertices identified by their IDs $1, 2,.., n$ respectively. Input In the first line, an integer $n$ is given. In the next $n$ lines, an adjacency list $Adj[u]$ for vertex $u$ are given in the following format: $u$ $k$ $v_1$ $v_2$ ... $v_k$ $u$ is vertex ID and $k$ denotes its degree. $v_i$ are IDs of vertices adjacent to $u$. Output As shown in the following sample output, print the adjacent-matrix representation of $G$. Put a single space character between $a_{ij}$. Constraints $1 \leq n \leq 100$ Sample Input 4 1 2 2 4 2 1 4 3 0 4 1 3 Sample Output 0 1 0 1 0 0 0 1 0 0 0 0 0 0 1 0	36,185
Score : 900 points Problem Statement Takahashi has an empty string S and a variable x whose initial value is 0 . Also, we have a string T consisting of 0 and 1 . Now, Takahashi will do the operation with the following two steps \|T\| times. Insert a 0 or a 1 at any position of S of his choice. Then, increment x by the sum of the digits in the odd positions (first, third, fifth, ...) of S . For example, if S is 01101 , the digits in the odd positions are 0 , 1 , 1 from left to right, so x is incremented by 2 . Print the maximum possible final value of x in a sequence of operations such that S equals T in the end. Constraints 1 \leq \|T\| \leq 2 \times 10^5 T consists of 0 and 1 . Input Input is given from Standard Input in the following format: T Output Print the maximum possible final value of x in a sequence of operations such that S equals T in the end. Sample Input 1 1101 Sample Output 1 5 Below is one sequence of operations that maximizes the final value of x to 5 . Insert a 1 at the beginning of S . S becomes 1 , and x is incremented by 1 . Insert a 0 to the immediate right of the first character of S . S becomes 10 , and x is incremented by 1 . Insert a 1 to the immediate right of the second character of S . S becomes 101 , and x is incremented by 2 . Insert a 1 at the beginning of S . S becomes 1101 , and x is incremented by 1 . Sample Input 2 0111101101 Sample Output 2 26	36,186
Score : 66 points Problem Statement Summer vacation ended at last and the second semester has begun. You, a Kyoto University student, came to university and heard a rumor that somebody will barricade the entrance of your classroom. The barricade will be built just before the start of the A -th class and removed by Kyoto University students just before the start of the B -th class. All the classes conducted when the barricade is blocking the entrance will be cancelled and you will not be able to attend them. Today you take N classes and class i is conducted in the t_i -th period. You take at most one class in each period. Find the number of classes you can attend. Constraints 1 \leq N \leq 1000 1 \leq A < B \leq 10^9 1 \leq t_i \leq 10^9 All t_i values are distinct. Input N , A and B are given on the first line and t_i is given on the (i+1) -th line. N A B t 1 : t N Output Print the number of classes you can attend. Sample Input 1 5 5 9 4 3 6 9 1 Sample Output 1 4 You can not only attend the third class. Sample Input 2 5 4 9 5 6 7 8 9 Sample Output 2 1 You can only attend the fifth class. Sample Input 3 4 3 6 9 6 8 1 Sample Output 3 4 You can attend all the classes. Sample Input 4 2 1 2 1 2 Sample Output 4 1 You can not attend the first class, but can attend the second.	36,187
Janken Master You are supposed to play the rock-paper-scissors game. There are $N$ players including you. This game consists of multiple rounds. While the rounds go, the number of remaining players decreases. In each round, each remaining player will select an arbitrary shape independently. People who show rocks win if all of the other people show scissors. In this same manner, papers win rocks, scissors win papers. There is no draw situation due to the special rule of this game: if a round is tied based on the normal rock-paper-scissors game rule, the player who has the highest programming contest rating (this is nothing to do with the round!) will be the only winner of the round. Thus, some players win and the other players lose on each round. The losers drop out of the game and the winners proceed to a new round. They repeat it until only one player becomes the winner. Each player is numbered from $1$ to $N$. Your number is $1$. You know which shape the other $N-1$ players tend to show, that is to say, you know the probabilities each player shows rock, paper and scissors. The $i$-th player shows rock with $r_i\%$ probability, paper with $p_i\%$ probability, and scissors with $s_i\%$ probability. The rating of programming contest of the player numbered $i$ is $a_i$. There are no two players whose ratings are the same. Your task is to calculate your probability to win the game when you take an optimal strategy based on each player's tendency and rating. Input The input consists of a single test case formatted as follows. $N$ $a_1$ $a_2$ $r_2$ $p_2$ $s_2$ ... $a_N$ $r_N$ $p_N$ $s_N$ The first line consists of a single integer $N$ ($2 \leq N \leq 14$). The second line consists of a single integer $a_i$ ($1 \leq a_i \leq N$). The ($i+1$)-th line consists of four integers $a_i, r_i, p_i$ and $s_i$ ($1 \leq a_i \leq N, 0 \leq r_i, p_i, s_i \leq 100,$ $r_i + p_i + s_i = 100$) for $i=2, ..., N$. It is guaranteed that $a_1, ..., a_N$ are pairwise distinct. Output Print the probability to win the game in one line. Your answer will be accepted if its absolute or relative error does not exceed $10^{-6}$. Sample Input 1 2 2 1 40 40 20 Output for Sample Input 1 0.8 Since you have the higher rating than the other player, you will win the game if you win or draw in the first round. Sample Input 2 2 1 2 50 50 0 Output for Sample Input 2 0.5 You must win in the first round. Sample Input 3 3 2 1 50 0 50 3 0 0 100 Output for Sample Input 3 1 In the first round, your best strategy is to show a rock. You will win the game with $50\%$ in this round. With the other $50\%$, you and the second player proceed to the second round and you must show a rock to win the game. Sample Input 4 3 2 3 40 40 20 1 30 10 60 Output for Sample Input 4 0.27 Sample Input 5 4 4 1 34 33 33 2 33 34 33 3 33 33 34 Output for Sample Input 5 0.6591870816	36,188
Score : 200 points Problem Statement N Snukes called Snuke 1 , Snuke 2 , ..., Snuke N live in a town. There are K kinds of snacks sold in this town, called Snack 1 , Snack 2 , ..., Snack K . The following d_i Snukes have Snack i : Snuke A_{i, 1}, A_{i, 2}, \cdots, A_{i, {d_i}} . Takahashi will walk around this town and make mischief on the Snukes who have no snacks. How many Snukes will fall victim to Takahashi's mischief? Constraints All values in input are integers. 1 \leq N \leq 100 1 \leq K \leq 100 1 \leq d_i \leq N 1 \leq A_{i, 1} < \cdots < A_{i, d_i} \leq N Input Input is given from Standard Input in the following format: N K d_1 A_{1, 1} \cdots A_{1, d_1} \vdots d_K A_{K, 1} \cdots A_{K, d_K} Output Print the answer. Sample Input 1 3 2 2 1 3 1 3 Sample Output 1 1 Snuke 1 has Snack 1 . Snuke 2 has no snacks. Snuke 3 has Snack 1 and 2 . Thus, there will be one victim: Snuke 2 . Sample Input 2 3 3 1 3 1 3 1 3 Sample Output 2 2	36,189
Height of a Tree Given a tree T with non-negative weight, find the height of each node of the tree. For each node, the height is the distance to the most distant leaf from the node. Input n s 1 t 1 w 1 s 2 t 2 w 2 : s n-1 t n-1 w n-1 The first line consists of an integer n which represents the number of nodes in the tree. Every node has a unique ID from 0 to n -1 respectively. In the following n -1 lines, edges of the tree are given. s i and t i represent end-points of the i -th edge (undirected) and w i represents the weight (distance) of the i -th edge. Output The output consists of n lines. Print the height of each node 0, 1, 2, ..., n-1 in order. Constraints 1 ≤ n ≤ 10,000 0 ≤ w i ≤ 1,000 Sample Input 1 4 0 1 2 1 2 1 1 3 3 Sample Output 1 5 3 4 5	36,190
Score : 600 points Problem Statement Given is a positive integer N . We will choose an integer K between 2 and N (inclusive), then we will repeat the operation below until N becomes less than K . Operation: if K divides N , replace N with N/K ; otherwise, replace N with N-K . In how many choices of K will N become 1 in the end? Constraints 2 \leq N \leq 10^{12} N is an integer. Input Input is given from Standard Input in the following format: N Output Print the number of choices of K in which N becomes 1 in the end. Sample Input 1 6 Sample Output 1 3 There are three choices of K in which N becomes 1 in the end: 2 , 5 , and 6 . In each of these choices, N will change as follows: When K=2 : 6 \to 3 \to 1 When K=5 : 6 \to 1 When K=6 : 6 \to 1 Sample Input 2 3141 Sample Output 2 13 Sample Input 3 314159265358 Sample Output 3 9	36,191
Score : 300 points Problem Statement You are given an integer N . Find the number of the positive divisors of N! , modulo 10^9+7 . Constraints 1≤N≤10^3 Input The input is given from Standard Input in the following format: N Output Print the number of the positive divisors of N! , modulo 10^9+7 . Sample Input 1 3 Sample Output 1 4 There are four divisors of 3! =6 : 1 , 2 , 3 and 6 . Thus, the output should be 4 . Sample Input 2 6 Sample Output 2 30 Sample Input 3 1000 Sample Output 3 972926972	36,192
Score : 1300 points Problem Statement A museum exhibits N jewels, Jewel 1, 2, ..., N . The coordinates of Jewel i are (x_i, y_i) (the museum can be regarded as a two-dimensional plane), and the value of that jewel is v_i . Snuke the thief will steal some of these jewels. There are M conditions, Condition 1, 2, ..., M , that must be met when stealing jewels, or he will be caught by the detective. Each condition has one of the following four forms: ( t_i = L , a_i , b_i ) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or smaller. ( t_i = R , a_i , b_i ) : Snuke can only steal at most b_i jewels whose x coordinates are a_i or larger. ( t_i = D , a_i , b_i ) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or smaller. ( t_i = U , a_i , b_i ) : Snuke can only steal at most b_i jewels whose y coordinates are a_i or larger. Find the maximum sum of values of jewels that Snuke the thief can steal. Constraints 1 \leq N \leq 80 1 \leq x_i, y_i \leq 100 1 \leq v_i \leq 10^{15} 1 \leq M \leq 320 t_i is L , R , U or D . 1 \leq a_i \leq 100 0 \leq b_i \leq N - 1 (x_i, y_i) are pairwise distinct. (t_i, a_i) are pairwise distinct. (t_i, b_i) are pairwise distinct. Input Input is given from Standard Input in the following format: N x_1 y_1 v_1 x_2 y_2 v_2 : x_N y_N v_N M t_1 a_1 b_1 t_2 a_2 b_2 : t_M a_M b_M Output Print the maximum sum of values of jewels that Snuke the thief can steal. Sample Input 1 7 1 3 6 1 5 9 3 1 8 4 3 8 6 2 9 5 4 11 5 7 10 4 L 3 1 R 2 3 D 5 3 U 4 2 Sample Output 1 36 Stealing Jewel 1, 5, 6 and 7 results in the total value of 36 . Sample Input 2 3 1 2 3 4 5 6 7 8 9 1 L 100 0 Sample Output 2 0 Sample Input 3 4 1 1 10 1 2 11 2 1 12 2 2 13 3 L 8 3 L 9 2 L 10 1 Sample Output 3 13 Sample Input 4 10 66 47 71040136000 65 77 74799603000 80 53 91192869000 24 34 24931901000 91 78 49867703000 68 71 46108236000 46 73 74799603000 56 63 93122668000 32 51 71030136000 51 26 70912345000 21 L 51 1 L 7 0 U 47 4 R 92 0 R 91 1 D 53 2 R 65 3 D 13 0 U 63 3 L 68 3 D 47 1 L 91 5 R 32 4 L 66 2 L 80 4 D 77 4 U 73 1 D 78 5 U 26 5 R 80 2 R 24 5 Sample Output 4 305223377000	36,193
Score : 100 points Problem Statement Takahashi is a user of a site that hosts programming contests. When a user competes in a contest, the rating of the user (not necessarily an integer) changes according to the performance of the user, as follows: Let the current rating of the user be a . Suppose that the performance of the user in the contest is b . Then, the new rating of the user will be the avarage of a and b . For example, if a user with rating 1 competes in a contest and gives performance 1000 , his/her new rating will be 500.5 , the average of 1 and 1000 . Takahashi's current rating is R , and he wants his rating to be exactly G after the next contest. Find the performance required to achieve it. Constraints 0 \leq R, G \leq 4500 All input values are integers. Input Input is given from Standard Input in the following format: R G Output Print the performance required to achieve the objective. Sample Input 1 2002 2017 Sample Output 1 2032 Takahashi's current rating is 2002 . If his performance in the contest is 2032 , his rating will be the average of 2002 and 2032 , which is equal to the desired rating, 2017 . Sample Input 2 4500 0 Sample Output 2 -4500 Although the current and desired ratings are between 0 and 4500 , the performance of a user can be below 0 .	36,194
Score : 800 points Problem Statement There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1 . The square at the i -th row from the top and the j -th column from the left contains a_{ij} . Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353 : The sum of the \|A\|\|B\| numbers contained in the intersection of the rows belonging to A and the columns belonging to B , is odd. Constraints 1 \leq N,M \leq 300 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M) All values in input are integers. Input Input is given from Standard Input in the following format: N M a_{11} ... a_{1M} : a_{N1} ... a_{NM} Output Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353 . Sample Input 1 2 2 0 1 1 0 Sample Output 1 6 For example, if A consists of the first row and B consists of both columns, the sum of the numbers contained in the intersection is 0+1=1 . Sample Input 2 2 3 0 0 0 0 1 0 Sample Output 2 8	36,195
F - ７歳教７歳の誕生日に"彼"は父から告げられた．「お前が７歳になったということは，私はもう引退だ．今日からお前が７歳教の長だ．７歳教の戒律により，７歳教の長が７歳の間だけ布教活動を行うことが認められている．この宇宙船を使って，よりたくさんの人々に７歳教の素晴らしさを広めてきなさい．」７歳教をよりたくさんの人に広めるために"彼"は，自分の周りの星についての情報を集めた． "彼"の星の周りには， n 個の惑星があり，惑星は 1, ... , n で番号付けされていることがわかった．惑星 i から惑星 j の間を移動するには， w_i_j (年)の時間がかかることもわかった．そして，それぞれの星で彼が７歳でいられる時間，つまり布教活動できる時間が異なることがわかった．それぞれの惑星上では，宇宙暦 l_i 年1月1日00:00:00以降 r_i 年1月1日00:00:00より前までの時間帯であれば7歳でいられる．たとえ一度ある星で７歳以外の年齢になっても，その星で後から７歳になった場合や，別の星で７歳になれば布教活動を再開することができる．しかしどの星でどれくらい，そしてどの順序で布教活動を行えばより多くの人に７歳教を伝えることができるのか， "彼"にはわからなかった．そこで"彼"はプログラミングが得意なあなたに助けを求めることにした．現在は宇宙暦0年1月1日00:00:00であり，"彼"は惑星 s にいる．惑星間を最適に移動・滞在した場合に布教活動が行える最長の年数，つまり"彼"が７歳でかつ惑星で過ごす最長の年数 T を求めてあげよう．ただし，年数 T には移動時間は含まれない．入力形式入力は以下の形式で与えられる． n s l_1 r_1 ... l_{n} r_{n} w_{1,1} w_{1,2} ... w_{1,n} ... w_{n,1} w_{n,2} ... w_{n,n} n は惑星の個数である． s は主人公が最初にいる惑星をあらわす． l_i と r_i はそれぞれ，惑星 i での7歳でいられる時間帯の下限と上限をあらわす． w_i_j は，惑星 i から惑星 j を移動するのにかかる時間をあらわす．入力はすべて整数である．出力形式答え T を出力せよ．制約 1 ≤ n ≤ 500 1 ≤ s ≤ n 0 ≤ l_i < r_i ≤ 10^8 0 ≤ w_{ij} ≤ 10^8 ( i ≠ j ) w_{ij} = 0 ( i = j ) 入出力例入力例 1 2 1 0 100 150 250 0 100 100 0 出力例 1 150 入力例 2 5 1 7 44 10 49 38 48 11 23 11 30 0 1 7 2 7 10 0 3 8 10 4 8 0 2 5 3 2 1 0 4 8 4 3 3 0 出力例 2 41	36,196
Fair Chocolate-Cutting You are given a flat piece of chocolate of convex polygon shape. You are to cut it into two pieces of precisely the same amount with a straight knife. Write a program that computes, for a given convex polygon, the maximum and minimum lengths of the line segments that divide the polygon into two equal areas. The figures below correspond to first two sample inputs. Two dashed lines in each of them correspond to the equal-area cuts of minimum and maximum lengths. Figure F.1. Sample Chocolate Pieces and Cut Lines Input The input consists of a single test case of the following format. $n$ $x_1$ $y_1$ ... $x_n$ $y_n$ The first line has an integer $n$, which is the number of vertices of the given polygon. Here, $n$ is between 3 and 5000, inclusive. Each of the following $n$ lines has two integers $x_i$ and $y_i$, which give the coordinates ($x_i, y_i$) of the $i$-th vertex of the polygon, in counterclockwise order. Both $x_i$ and $y_i$ are between 0 and 100 000, inclusive. The polygon is guaranteed to be simple and convex. In other words, no two edges of the polygon intersect each other and interior angles at all of its vertices are less than $180^\circ$. Output Two lines should be output. The first line should have the minimum length of a straight line segment that partitions the polygon into two parts of the equal area. The second line should have the maximum length of such a line segment. The answer will be considered as correct if the values output have an absolute or relative error less than $10^{-6}$. Sample Input 1 4 0 0 10 0 10 10 0 10 Sample Output 1 10 14.142135623730950488 Sample Input 2 3 0 0 6 0 3 10 Sample Output 2 4.2426406871192851464 10.0 Sample Input 3 5 0 0 99999 20000 100000 70000 33344 63344 1 50000 Sample Output 3 54475.580091580027976 120182.57592539864775 Sample Input 4 6 100 350 101 349 6400 3440 6400 3441 1200 7250 1199 7249 Sample Output 4 4559.2050019027964982 6216.7174287968524227	36,197
Problem I: Aaron と Bruce Aaron は凶悪な犯罪者である．彼は幾度も犯罪を繰り返しながら（万引き2回，のぞき16回，下着泥棒256回，食い逃げ65,536回）も，その人並み外れた身体能力を用いて警察の手から逃れ続けてきた． Bruce は警察官である．彼は突出した運動能力は持っていないが，写真撮影が趣味であり，彼の撮った写真が雑誌に載るほどの腕前を持っている．ある日，Bruce は山奥に写真撮影をしに来た．すると偶然 Aaron のアジトを突き止めてしまった． Bruce が逃げる Aaron を追っていくと，彼らは落とし穴に落ちて古代遺跡の中に迷い込んでしまった．古代遺跡の中はいくつかの部屋と，部屋どうしを結ぶ通路で構成されている．古代遺跡に M 個の部屋があるとき，遺跡内の部屋にはそれぞれ 0 から M −1 までの番号がつけられている． Aaron は逃げている間に時効を迎えるかもしれないと考えたので， Bruce が最適に移動したときに一番長い間逃げ続けられるように遺跡の中を移動する． Bruce は早く Aaron を写真に収めたいので， Aaron が最適に移動したときに一番早く Bruce を写真に収められるように遺跡の中を移動する． Aaron と Bruce は順番に行動する．最初は Aaron の番とする．それぞれの順番のとき，隣接している部屋のどれか1つに移動，もしくはその場にとどまることができる． Aaron と Bruce が同じ部屋に入ったとき， Bruce は Aaron を撮影するものとする． Bruce が Aaron を撮影するのにどれくらいの時間がかかるかを求めて欲しい．時間はターン数で表すこととし， Aaron と Bruce がともに1回行動し終わったら1ターンと数える．例えば，図5のような状況のとき， Aaron は部屋5に逃げ込めば Bruce は4ターンでたどり着くが， Aaron が部屋7に逃げ込めば Bruce はたどり着くのに5ターンかかる． Aaron にとっては部屋7に逃げ込むことで一番長く逃げ続けられるので答えは5ターンとなる．図5: Aaron が5ターン逃げ続けられる例．また，図6のような状況のとき， Aaron が Bruce から遠ざかるように部屋を移動することでいつまでも逃げ回ることができる．図6: Aaron がいつまでも逃げ続けられる例． Input 入力の最初の行にデータセット数を表す数 N (0 < N ≤ 100) が与えられる．次の行から N 個のデータセットが続く．各データセットは古代遺跡の形状と Aaron と Bruce の初期位置からなる．初めに，古代遺跡の部屋の数 M (2 ≤ M ≤ 50) が与えられる．次に要素数 M × M の行列が与えられる．各行列の要素は 0 もしくは 1 であり， i 行目の j 番目の数字が 1 ならば，部屋 i と部屋 j は通路でつながっているということを意味する（ただし，行列の行番号と列番号は0から数える）．行列の ( i , j ) 成分と ( j , i ) 成分の値は必ず等しく， ( i , i ) 成分の値は 0 である．続いて，2つの整数 a , b が与えられる．各整数はそれぞれ Aaron の初期位置の部屋番号 (0 ≤ a < M ) と Bruce の初期位置の部屋番号 (0 ≤ b < M ) を示す． a と b の値は必ず異なる． Output 各データセットごとに，Bruce が Aaron を撮影するのに何ターンかかるかを 1行で出力せよ．どれだけたっても撮影できない場合は “ infinity ” と出力せよ． Sample Input 6 8 0 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 3 0 4 0 1 1 0 1 0 0 1 1 0 0 1 0 1 1 0 1 0 5 0 1 0 1 0 1 0 0 1 0 0 0 0 0 1 1 1 0 0 0 0 0 1 0 0 2 0 5 0 1 0 0 1 1 0 1 1 1 0 1 0 1 0 0 1 1 0 1 1 1 0 1 0 2 4 5 0 1 0 1 0 1 0 1 1 0 0 1 0 0 1 1 1 0 0 1 0 0 1 1 0 3 0 5 0 1 0 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 0 1 0 0 4 Output for the Sample Input 5 infinity infinity 2 infinity 1	36,198
Problem Statement You are given two integers a and b ( a≤b ). Determine if the product of the integers a , a+1 , … , b is positive, negative or zero. Constraints a and b are integers. -10^9≤a≤b≤10^9 Partial Score In test cases worth 100 points, -10≤a≤b≤10 . Input The input is given from Standard Input in the following format: a b Output If the product is positive, print Positive . If it is negative, print Negative . If it is zero, print Zero . Sample Input 1 1 3 Sample Output 1 Positive 1×2×3=6 is positive. Sample Input 2 -3 -1 Sample Output 2 Negative (-3)×(-2)×(-1)=-6 is negative. Sample Input 3 -1 1 Sample Output 3 Zero (-1)×0×1=0 .	36,199
Combination of Number Sequences 0 から 9 までの整数を使った n 個の数の並び k 1 , k 2 , ..., k n を考えます。正の整数 n と s を読み込んで、 k 1 + 2 × k 2 + 3 × k 3 + ... + n × k n = s となっているような n 個の数の並びが何通りあるかを出力するプログラムを作成してください。ただし、1 つの「 n 個の数の並び」には同じ数が 2 回以上現われないものとします。 Input 入力は複数のデータセットからなります。各データセットとして、 n (1 ≤ n ≤ 10) と s (0 ≤ s ≤ 10,000)が空白区切りで１行に与えられます。データセットの数は 100 を超えません。 Output データセットごとに、 n 個の整数の和が s になる組み合わせの個数を１行に出力します。 Sample Input 3 10 3 1 Output for the Sample Input 8 0	36,200

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