Does culture define institutions or do institutions define culture?

Does culture define institutions or do institutions define culture? What do you think? It is like a question to ask you whether chickens come first or eggs.

In my opinion, culture and institutions are interdependent. Nonetheless, I feel that culture defines institution first is a more logical statement. Why do I say so? When we turn back the pendulum to the ancient time where humans were first born or made into this world, the institutions did not exist. I believe that the first generation of humans lived in an environment which was totally on their own. They did not have more companions. They lived their own lives, they hunted for food, and they learned to survive. As time passed, they gave birth, they learned to communicate, and most importantly, they learned to value things differently. Distinctive beliefs were thus shaped, various lifestyles were formed.

Birds of a feather flock together. As the community went bigger, they formed their own tribes. The tribe might share the same physical appearance like skin color or hair color, similar communication ways like language, common lifestyles like food preference, values, rules, religions and beliefs. These are all the essence of a culture. Leaders were then chosen to lead the community. This is what I believe the first generation of institution might be. As the civilization progressed, the cultural process perpetuated. The institutions shaped the culture in return. The new-born children were raised up in the culture that was being upheld by the community. Then they took the leadership when they grew up and culturally influenced the next generation.

This is how I believe the institutions were defined first by the culture.