H. Olympic Team Buildingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputIron and Werewolf are participating in a chess Olympiad, so they want to practice team building. They gathered n players, where n is a power of 2, and they will play sports. Iron and Werewolf are among those n people.One of the sports is tug of war. For each 1\leq i \leq n, the i-th player has strength s_i. Elimination rounds will be held until only one player remains — we call that player the absolute winner.In each round:   Assume that m>1 players are still in the game, where m is a power of 2.  The m players are split into two teams of equal sizes (i. e., with m/2 players in each team). The strength of a team is the sum of the strengths of its players.  If the teams have equal strengths, Iron chooses who wins; otherwise, the stronger team wins.  Every player in the losing team is eliminated, so m/2 players remain. Iron already knows each player's strength and is wondering who can become the absolute winner and who can't if he may choose how the teams will be formed in each round, as well as the winning team in case of equal strengths.InputThe first line contains a single integer n (4 \leq n \leq 32) — the number of players participating in tug of war. It is guaranteed that n is a power of 2.The second line consists of a sequence s_1,s_2, \ldots, s_n of integers (1 \leq s_i \leq 10^{15}) — the strengths of the players.OutputIn a single line output a binary string s of length n — the i-th character of s should be 1 if the i-th player can become the absolute winner and it should be 0 otherwise.ExamplesInput
4
60 32 59 87
Output
1001
Input
4
100 100 100 100
Output
1111
Input
8
8 8 8 8 4 4 4 4
Output
11110000
Input
32
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Output
00000000000000001111111111111111
Input
16
1 92875987325987 1 1 92875987325986 92875987325985 1 92875987325988 92875987325990 92875987325989 1 1 92875987325984 92875987325983 1 1
Output
0100110111001000
NoteIn the first example, players 1 and 4 with their respective strengths of 60 and 87 can become the absolute winners.Let's describe the process for player 1. Firstly, we divide the players into teams [1,3] and [2,4]. Strengths of those two teams are 60+59=119 and 32+87=119. They they are equal, Iron can choose to disqualify any of the two teams. Let his choice be the second team.We are left with players 1 and 3. Since 1 has greater strength (60>59) they win and are declared the absolute winner as they are the last remaining player.In the third example, the strengths of the remaining players may look like [8,8,8,8,4,4,4,4] \rightarrow [8,8,4,4] \rightarrow [8,4] \rightarrow [8]. Each person with strength 8 can become the absolute winner and it can be proved that others can't.
4
60 32 59 87

1001 
['brute force', 'meet-in-the-middle', '*3500']