In a small football league, teams are awarded 5 points for winning a match, 3 points for a draw and 1 point for losing. The team with the most points after 12 matches wins a prize.Team A win 6 of their matches and have half as many draws. The rest of the matches they lose.Team B win as many matches as Team A lose, but all the rest of their matches are draws and they don’t lose a single game.Team C and D both lose 10 matches, but Team C wins the rest and Team D draws the rest.Team E wins 1 more match than Team A, but draws 2 matches and loses the rest.Which team wins the prize?

A total of 11 teams participated in a hockey tournament in which every team played exactly one match with every other team. In any match, a team gets four points for a win, three points for a draw and two points for a loss. The total score of no two teams was the same at the end of the tournament. If the number of points of the team with the highest total score is 35, then which of the following could be the number of points of the team with the least total score?

In a tournament, a team has played 40 matches so far and won 30%30% of them. If they win 60%60% of the remaining matches, their overall win percentage will be 50%50%. Suppose they win 90%90% of the remaining matches, then the total number of matches won by the team in the tournament will be.

A football team played 38 games.19 games were played at home and the rest were played away.The team won a total of 21 games.They drew 4 games away.2 of the 10 games they lost were at home.Copy and complete the two way table.

If the losses of player A are the game of the player B, then the game is known as

Three friends gathered to play a few games of chess together.In every game, two of them play against each other. The winner gets 22 points while the loser gets 00, and in case of a draw, both players get 11 point each. Note that the same pair of players could have played any non-negative number of times (possibly zero). It is also possible that no games were played at all.You've been told that their scores after all the games were played were p1𝑝1, p2𝑝2 and p3𝑝3. Additionally, it is guaranteed that p1≤p2≤p3𝑝1≤𝑝2≤𝑝3 holds.Find the maximum number of draws that could have happened and print it. If there isn't any way to obtain p1𝑝1, p2𝑝2 and p3𝑝3 as a result of a non-negative number of games between the three players, print −1−1 instead.InputEach test contains multiple test cases. The first line contains the number of test cases t𝑡 (1≤t≤5001≤𝑡≤500). The description of the test cases follows.The first line of each test case contains three integers p1𝑝1, p2𝑝2 and p3𝑝3 (0≤p1≤p2≤p3≤300≤𝑝1≤𝑝2≤𝑝3≤30) — the scores of the three players, sorted non-decreasingly.OutputFor each testcase, print one number — the maximum possible number of draws that could've happened, or −1−1 if the scores aren't consistent with any valid set of games and results.ExampleinputCopy70 0 00 1 11 1 11 1 23 3 33 4 51 1 10outputCopy01-12-162NoteIn the first example, no games were played at all, so no draws could occur either.For the second example, exactly one game occurred between the second and the third player and it ended in draw, so the answer is 11.It's easy to see that there's no set of games achieving the scores in third example, so the answer for it is −1−1.