555 timer Relay driver with TTL input

Hello,
I want to drive a 12v relay off a 555 timer after being triggered by a 12v PIR sensor. The sensor has a 3.3V TTL output which goes HI when the sensor is triggered. Once the sensor turns off the TTL output returns to 0V.
-I want the Relay to turn on for 3 minutes (can be adjustable) after being triggered.

I think I need a monostable circuit & I know the trigger needs a low input, but I'm unable to figure out how to put this together.
Is anyone able to fill in the gaps or provide a known working circuit?



Thnaks in advance,
M.W.

The blue and yellow highlited parts are optional. Those allow the PIR to retrigger the 555 and keep the relay active 3 more minutes for each PIR excitation. Without them, the relay will turn off after 3 minutes. And, once off, it can be retriggered for the next PIR excitation.

Thats fantastic - exactly what I'm after.
Thanks gophert.