There were in fact more than one Mew. Millions of years ago when the planet was still young, there were seventeen Mews, each of them similar, but different at the same time. Each Mew has its own story to tell.
The first Mew decided to travel to a large mountain that it saw when it was flying around the region. This particular mountain seemed different than any other mountain it had seen before. Suddenly there was a loud rumbling noise and the Mew did not know why. The noise was followed by a huge explosion filled with fire and smoke. The surprised Mew had no time to escape and was engulfed by lava. But the intense temperatures didn't harm it. In fact, the Mew realized it enjoyed the heat. This Mew became the ancestor of Fire-types.
The second Mew saw the beauty of the sunrise and wished to visit the sun. Everyday it soared towards that ball of light, hoping to someday reach it. But no matter how high or how fast it flew, it could never seem to get any closer. It even used its Transform ability to give itself a pair of wings, but that still did no good. Yet the Mew would not give up. It enjoyed being amongst the clouds and thought that it would reach its goal if it kept flying. This Mew became the ancestor of Flying-types.
Another Mew was the complete opposite. It was actually afraid of heights and preferred to stay close to the ground where it felt safe and secure. It eventually lost the ability to fly, but that didn't matter. Its legs and arms became more powerful due to the amount of time it spent digging and it realized the world underneath the earth's surface was fascinating and full of wonder. This Mew became the ancestor of Ground-types.
The next Mew decided to travel north to see what was there. After traveling for miles and miles, it realized the trees where getting smaller and fewer. Eventually, the landscape was filled with nothing but white stuff. What is this stuff? It felt very cold and took some getting used to, but it was very fun to play with. And when night came, a beautiful aurora filled the sky. The Mew decided this would be a wonderful place to spend the rest of its days. This Mew became the ancestor of Ice-types.
The fifth Mew looked down from the sky and saw the endless beauty of nature. From tiny flower to massive tree, each plant was a work of art. The Mew learned about the importance of sunlight, soil, and water. It used its knowledge to build its own garden that eventually bloomed and was one of the most beautiful sights on earth. This Mew became the ancestor of Grass-types.
One Mew got caught in a fierce storm and sought shelter underneath a tall tree. This was a bad decision since the tree was demolished by a tremendous bolt of lightning with the Mew still under it. Fortunately, the Mew came out uninjured, yet it felt different than before as if it had been re-energized. This Mew became the ancestor of Electric-types.
Our next Mew decided to travel across the ocean to see what was on the other side. But it had a bad sense of direction and quickly became lost. So it changed its mind. Instead of exploring what was across the sea, it would explore what was underneath it. So it surrounded itself with an air bubble and plunged into the depths. The underwater world was a huge and marvelous place. The Mew spent a very long time there and eventually it used Transform to give itself a set of gills and fins so it could swim without its air bubble. This Mew became the ancestor of Water-types.
There was a pair of Mew who were friends and decided to have an adventure in the mountains. They discovered a cave and were curious what was inside. The cave stretched on for what seemed like an eternity, but it didn't seem to hold anything interesting. They were just about to turn and leave when suddenly, the roof of the cave started collapsing! Not only were they trapped inside the cave, but they were also separated from each other. The boulders between them were big and nearly impossible to move. One of the Mew started pounding away at the boulders again and again. The other Mew started chiseling away at the boulders with its feet and tail. This continued for days, but they were eventually able to break through and escape.
The first Mew felt its skin had become tough and hard from all the work it went through. It became the ancestor of Rock-types.
The other felt its limbs had become sharp like blades. It became the ancestor of Steel-types.
The next two Mew both lived in a forest, though they weren't close friends.
One of the two was always trying out new things to eat. One day it saw a bunch of bright red mushrooms growing near the base of a tree. It took a few bites and realized they were the most delicious things it ever ate. But these mushrooms also made it very ill since they had toxins in their spores. Yet the Mew wasn't willing to give up. It ate the mushrooms in moderation, a little each day until it gained an immunity. It became the ancestor of Poison-types.
The other forest-dwelling Mew preferred flowers instead of mushrooms. More specifically it loved the sweet nectar from certain flowers, but getting at the nectar proved difficult for something that was not adapted to this style of feeding. Over time, it learned to Transform its body to give it better access to nectar and it also learned the pollination process so it can grow even more flowers. This Mew became the ancestor of Bug-types.
There was another Mew who was quite shy and preferred to be alone. In order to avoid the others, it slept in the day and only woke up when the sun set. Nighttime gave the Mew the peace and solitude it wanted, but it was also hard to see. The Mew learned to adjust its sense of sight, hearing, and smell to the world of darkness and eventually became the ancestor of Dark-types.
The thirteenth Mew wasn't as strong as the others when it came to Psychic abilities. Its mental strength was lacking and that made it feel ashamed to be around the others. So it traveled somewhere secret where it can focus on its physical strength instead. For months on end, it trained and built up the muscles in its body until it was proud of its new power. This Mew became the ancestor of Fighting-types.
Another Mew was very friendly and popular with the other Mews. It was constantly happy and loved to play games and have fun. But its body was frail and it eventually became sick. Despite all the help its friends tried to give, the Mew never recovered and eventually perished. Its friends wept and cried, but not all was lost. The Mew was not ready to leave the world of the living just yet and returned in a spirit form so it would always be with its friends. This Mew became the ancestor of Ghost-types.
The next Mew wasn't quite as friendly as the last. In fact, it was quite mean and aggressive. Since it was disliked by the others, it flew off to a distant land. It eventually made its home in a little den in the side of a mountain. It defended its territory fiercely and attacked anything that came to close. Meanwhile it spent the rest of its time training to become stronger. This Mew became the ancestor of Dragon-types.
The sixteenth Mew didn't really stand out in any way. It didn't travel to an exotic land or have any unusual habits. It was simply not special and despite that, it was perfectly fine with it. Not surprisingly, it became the ancestor of Normal-types.
The final Mew is the only one that still exists to this day. After all these eons it still retained its original Psychic-type and now it travels around the world watching the vast diversity of Pokemon that came from friends it once knew.
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