Find the least number which satisfies the following conditions:
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- It is a perfect square.
- If you remove the first digit of the number, the remaining number is still a perfect square.
- If you remove the first two digits of the number, the remaining number is still a perfect square.
- If you remove the last digit of the number, the remaining number is 1 more than a perfect square.
- The sum of its digits is 1 more than a perfect square.

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