Let  $f:A\to A,$   where  $A=\{1,2,3,4,5,6,7\}$  , then the number of functions ${ }^{\text{'}}{f}^{\text{'}}$ such that  $f\left(f\left(f\left(x\right)\right)\right)=x$  $\forall x\in A$  is ______ 
 

  $$${ }^7{C}_7{+}^7{C}_1[10\times 2\times 2]{+}^7{C}_4\times 2$

(1)Every element of A  satisfy $f\left(x\right)=x$ in identity function

(ii)Function can be identity function for four elements in $\left({ }^7{C}_4\right)2=70$

(iii)Function f(x) is mapped to only one element to itself in $7C1\left(\frac{6!\times 4}{3!3!2!}\right)=280$

Total =351