L is sure that Light is kira and Misa is second Kira . He randomly selects two permutation of $1$ to $N$ and store it in $A[0]$,$A[1]$,...$A[N-1]$ and $B[0]$,$B[1]$,...$B[N-1]$. All permutations are equally probable . Now he randomly selects a integer $X$ , $0$ <= $X$ < $N$ , and shifts permutation B to left by $X$ .

For Example - $[ 2,3,1,4,5 ]$ be a permutation , shifting it left by 2 will result $[ 1,4,5,2,3 ]$.

He defines another sequence $g[i]$ = $(A[i] * 1) mod B[i] + (A[i] * 2) mod B[i] + (A[i] * 3) mod B[i] ...... (A[i] * B[i]) mod B[i]$ .

Find expected value of $g[0]+g[1]+ ........ + g[N-1]$ for $N$ = $1111$.

Answer greatest integer of expected value.