 Complete the following phrase:  In response, an Eight Nation Alliance of American, Austro-Hungarian, British, French, German, Italian, Japanese, and Russian troops was organized to lift the siege. The Eight-Nation Alliance, after being initially turned back by the Boxer militia and allied Imperial Chinese military elements brought 20,000 armed troops to China, defeated the Imperial Army in Tianjin, and arrived in Beijing on 14 August, relieving the 