MEXICO CITY, Mexico (AFP) — Thousands of singing, flag-waving people packed a downtown square to celebrate Claudia Sheinbaum’s ground-breaking victory as Mexico’s first woman president.

Maria de los Angeles Gordillo, a 37-year-old member of the Tojolabal Indigenous community, said she was moved to tears as she listened to Sheinbaum speak overnight Sunday into Monday.

“I’m here to celebrate this historic moment for our country and especially for women who carry these inequalities on their skin,” she said.

Gordillo stood amid the crowd at the Zocalo, the main plaza in the capital city of this country plagued by drug cartels and gender-based violence that claims the lives of 10 women or girls on average every day.

Sheinbaum, a scientist by training, won around 58-60 percent of votes, according to preliminary official results from the National Electoral Institute, which estimated turnout at 60 percent.

That was more than 30 percentage points ahead of her main opposition rival Xochitl Galvez, and some 50 percentage points ahead of the only man running, centrist Jorge Alvarez Maynez.

Gordillo spoke shortly after Sheinbaum gave a victory speech in the Zocalo, as supporters of the ruling leftist Morena party shouted “We did it!”

Some women carried cardboard flags with a photo of Sheinbaum and the phrase “Llegamos todas”, her mantra during the election campaign. It translates roughly as “all of us women will make it.”

Revelers both male and female shouted “president! president!” as some raised their fist in the air.

Gordillo said Mexico faces many challenges but this is a moment of great change to address violence against women, among other problems.

“The fact that we have a woman president implies that we are making progress to change so many sad realities, because there are a lot of women missing,” she said.

More than 450,000 people have been murdered and tens of thousands have gone missing since the government deployed the army to fight drug trafficking in 2006.

Sheinbaum, the former mayor of Mexico City, will take office in October as leader of a country with a long history of male domination and mistreatment of women. Another big issue she will address is the disparity between what men and women earn.

Maria Fernanda Vela, 27, said it was a milestone that Mexicans chose a female president by a landslide.

“It is beautiful. It is an inspiration that in such a male chauvinist country, a woman has taken the top job. It fills your heart with pride,” said Vela.

On the sidelines of the celebration, a vendor sold dolls mimicking Sheinbaum and the popular outgoing president Andres Manuel Lopez Obrador.

People waved the red white and green flag of Mexico and the Morena party.