I can't add my gmail to the Mail app

So my the email account synced to my Mail app on my iPhone 6 stopped syncing mails whenever I check the app suddenly. I went to Settings--Mail, Contacts, Calendars, deleted which then wiped out all my contacts because they are in my gmail's account.

I tried setting it back up but it kept going to the main menu where you see Yahoo, AOL, Google, iCloud, Exchange, etc., options are.

It won't let me sync my gmail to the mail app. What's going on?