Input: Hoping to snap a two-game losing streak, the Broncos remained on home ground for an AFC West duel against the Oakland Raiders. The Broncos grabbed the early lead, with quarterback Peyton Manning throwing a 22-yard touchdown pass to tight end Joel Dreessen. The Raiders responded, with a 38-yard field goal by placekicker Sebastian Janikowski, but the Broncos countered, with a 21-yard field goal by placekicker Matt Prater at the end of the first quarter. A 24-yard field goal by Janikowski just before halftime was the only scoring play of the second quarter. The Broncos' offense exploded in the third quarter, with Manning connecting on a 17-yard touchdown pass to wide receiver Eric Decker, followed by a 2-yard touchdown run by running back Willis McGahee and a 14-yard touchdown pass from Manning to running back Lance Ball. Prater added field goals of 43 and 53 yards in the fourth quarter. With the win, the Broncos snapped a four-game home losing streak against the Raiders. Center J. D. Walton suffered a dislocated ankle late in the second quarter, and was placed on the season-ending injured reserve the following day (October 1).

Question: Were more yards of field goals kicked in the first or second half?

Input: Trying to snap a two-game losing skid, the Chiefs flew to the RCA Dome for a Week 12 intraconference duel against the defending Super Bowl champion Indianapolis Colts, in a rematch of last year's wildcard battle. This would be the game in which second-year quarterback Brodie Croyle would be given the start. After a scoreless first quarter, Kansas City struck first with kicker Dave Rayner getting a 47-yard field goal. The Colts would tie the game before halftime as kicker Adam Vinatieri managed to get a 27-yard field goal. In the third quarter, Indianapolis took the lead as RB Joseph Addai got a 3-yard TD run. The Chiefs would respond and tie the game with Croyle completing a 19-yard TD pass to rookie WR Dwayne Bowe. Unfortunately, in the fourth quarter, the Colts sealed the win as Vinatieri nailed the game-winning 24-yard field goal. The game was also the final outing of Priest Holmes, who suffered a neck injury in the fourth quarter. Holmes announced his retirement later into the week on November 21.

Question: How many more field goals did Adam Vinatieri score compared to Dave Rayner?

Input: In the following years, the Luneburg countryside was devastated by numerous battles and campaigns. These, however, were only partly due to the succession conflict - in addition there was wanton arson and looting by robber barons. In addition to the Ascanians and the Welfs, foreign towns and princes were increasingly involved as allies. Thus Magnus entered into a military alliance with the Danish king. In 1373, at an specially arranged meeting in Pirna, an imperial mediation attempt took place. Since Magnus did not appear, however, the Imperial Ban against him was renewed and fighting continued. In 1373, Duke Magnus was killed in a battle at Leveste on the Deister on 25 July 1373. After his death, a treaty - the Reconciliation of Hanover - was agreed between Wenceslas and his nephew Albert, on the one hand, and the widow of Magnus II and her sons on the other. According to the treaty, the estates of the Principality were to pay homage both to the Welfs and to the Ascanians, and the two noble houses would govern the state alternately. Initially, the land would be given to the two Ascanians from Wittenberg, and after their death it would go to the sons of the fallen Duke Magnus II. After their death, rule of the Principality was to revert to the Ascanians. In order to underpin the agreement, in 1374 Albert of Saxe-Luneburg married Catharina, the widow of Magnus II. The two still underage sons were also married in 1386 to members of the Ascanian house. Frederick of Brunswick-Luneburg married Anna of Saxe-Wittenberg and Bernard of Brunswick-Luneburg married Margareta of Saxony, both women were daughters of Wenceslas. The treaty also envisaged the creation of a statutory body representing the estates, which was to supervise the treaty.

Question: Anna of Saxe-Wittenberg was the child of who?

Input: The exact origin of the 260-day count is not known, but there are several theories. One theory is that the calendar came from mathematical operations based on the numbers thirteen and twenty, which were important numbers to the Maya. The numbers multiplied together equal 260. Another theory is that the 260-day period came from the length of human pregnancy. This is close to the average number of days between the first missed menstrual period and birth, unlike Naegele's rule which is 40 weeks between the last menstrual period and birth. It is postulated that midwives originally developed the calendar to predict babies' expected birth dates. A third theory comes from understanding of astronomy, geography and paleontology. The mesoamerican calendar probably originated with the Olmecs, and a settlement existed at Izapa, in southeast Chiapas Mexico, before 1200 BCE. There, at a latitude of about 15 N, the Sun passes through zenith twice a year, and there are 260 days between zenithal passages, and gnomons , were found at this and other sites. The sacred almanac may well have been set in motion on August 13, 1359 BCE, in Izapa.

Question:
How many theories exist to explain the origin of the 260-day count?