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$f(x)$ is a polynomial with integer coefficients. We have:

$f(1)=1$

$f(2)=4$

$f(3)=9$

$f(4)=16$

$f(5)=25$

$f(6)=36$

$f(7)=49$

$f(8)=64$

$f(9)=81$

$f(10)=100$

The number of functions $f(x)$ satisfying the above conditions is: