Okay so I bought the iphone brought it home and the battery died. Then I charged for awhile and it turn back on.  After that it randomly shuts down and restart again. the battery icon shows fully charge with 1% of battery...then after awhile it shuts off again and restarted.. I don't even know whether the phone is charging or not? what should I do now?

I just did a trial and error and it only shuts down and restart if I charge it..