input: Please answer the following: Extract the answer to the question from the following context. Question: What is another word for average? Context: The problem of the direction of time arises directly from two contradictory facts. Firstly, the fundamental physical laws are time-reversal invariant; if a cinematographic film were taken of any process describable by means of the aforementioned laws and then played backwards, it would still portray a physically possible process. Secondly, our experience of time, at the macroscopic level, is not time-reversal invariant. Glasses can fall and break, but shards of glass cannot reassemble and fly up onto tables. We have memories of the past, and none of the future. We feel we can't change the past but can influence the future.
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output: directly

input: Please answer the following: Extract the answer to the question from the following context. Question: Which Asian nation was able to play different powers against each other? Context: In some rare cases, such as with Ethiopia and Qing Dynasty China, the local governments were able to use the treaties to at least mitigate the impact of European colonization. This involved learning the intricacies of European diplomatic customs and then using the treaties to prevent a power from overstepping their agreement or by playing different powers against each other.
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output: China

input: Please answer the following: Extract the answer to the question from the following context. Question: What prevents a given region from being a true vacuum? Context: Vacuum is space void of matter. The word stems from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicists often discuss ideal test results that would occur in a perfect vacuum, which they sometimes simply call "vacuum" or free space, and use the term partial vacuum to refer to an actual imperfect vacuum as one might have in a laboratory or in space. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object as being in what would otherwise be a vacuum.
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output: matter

input: Please answer the following: Extract the answer to the question from the following context. Question: What was it called when the Americans stayed after the treaty? Context: The Treaty of Guadalupe Hidalgo, signed on February 2, 1848, by American diplomat Nicholas Trist and Mexican plenipotentiary representatives Luis G. Cuevas, Bernardo Couto, and Miguel Atristain, ended the war, gave the U.S. undisputed control of Texas, and established the U.S.Mexican border of the Rio Grande. As news of peace negotiations reached the state, new call to arms began to flare among the people of the state. But as the Mexican officials in Chihuahua heard that General Price was heading back to Mexico with a large force comprising several companies of infantry and three companies of cavalry and one division of light artillery from Santa Fe on February 8, 1848, Angel Trias sent a message to Sacramento Pass to ask for succession of the area as they understood the war had concluded. General Price, misunderstanding this as a deception by the Mexican forces, continued to advance towards the state capital. On March 16, 1848 Price began negotiations with Angel Trias, but the Mexican leader responded with an ultimatum to General Price. The American forces engaged with the Mexican forces near Santa Cruz de los Rosales on March 16, 1848. The Battle of Santa Cruz de los Rosales was the last battle of the MexicanAmerican War and it occurred after the peace treaty was signed. The American forces maintained control over the state capital for three months after the confirmation of the peace treaty. The American presence served to delay the possible succession of the state which had been discussed at the end of 1847, and the state remained under United States occupation until May 22, 1848.
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output:
occupation