calculate sum and average of rows that share a common identifier

I have an m by n matrix S and an m x 1 vector N with identifiers, one number (integer) in N for each row in S.

I want to calculate the average for those rows in S that have the same identifier in N.

Example: S=[1 2; 3 4; 5 6; 7 8; 9 10];

N=[1 6 6 53 53]';

Desired result: A=[1 2 ; 4 5 ; 8 9]

A(1,:)=average of row 1 in S

A(2,:)=average of rows 2 and 3 in S (they have a common identifier "6")

A(3,:)=average of rows 4 and 5 in S (they have a common identifier "53")

I can of course run a for loop, but it is quite a bit of data, so I thought it might be possible to use matlab's clever matrix notation.

Any suggestions?