Background: Gigi [ZiZi] is a 1958 American musical-romance film directed by Vincente Minnelli processed using MGM's Metrocolor. The screenplay by Alan Jay Lerner is based on the 1944 novella of the same name by Colette. The film features songs with lyrics by Lerner and music by Frederick Loewe, arranged and conducted by Andre Previn. In 1991, Gigi was selected for preservation in the United States National Film Registry by the Library of Congress as being "culturally, historically, or aesthetically significant".
Context: In late April, Freed and Minnelli and their respective entourages arrived in Paris. The weather had become unseasonably hot, and working in unair-conditioned hotel rooms was uncomfortable. Minnelli began scouting locations while Freed and Lerner discussed the still incomplete script. Lerner had taken liberties with Colette's novella; the character of Honore, nonexistent in the original book and very minor in the Loos play, was now a major figure. Gigi's mother, originally a significant character, was reduced to a few lines of dialogue delivered off-screen. Lerner also expanded the focus on Gigi's relationship with her grandmother.  By mid-July, the composers had completed most of the score, but still were missing the title tune. Loewe was at the piano while Lerner was indisposed in the bathroom, and when the former began playing a melody the latter liked, he later recalled he jumped up, "[his] trousers still clinging to [his] ankles, and made his way to the living room. 'Play that again,' he said. And that melody ended up being the title song for Gigi."  In September, the cast and crew flew to California, where several interior scenes were filmed, among them the entire scene in Maxim's, which included a musical number by Jourdan. Lerner was unhappy with the look of the scene as it had been shot by Minnelli, and at considerable expense, the restaurant was recreated on a soundstage and the scene was reshot by director Charles Walters, since Minnelli was overseas working on a new project.  The film title design uses the artwork of Sem's work from the Belle Epoque.
Question: Was it easy to come up with the title tune for the film?. Whats the answer?
By mid-July, the composers had completed most of the score, but still were missing the title tune.