Problem Statement

For two sets of integers, $A$ and $B$, such that $A \\cap B = \\emptyset$, we define $f(A,B)$ as follows.

• Let $C=(C_1,C_2,\\dots,C_{|A|+|B|})$ be a sequence consisting of the elements of $A \\cup B$, sorted in ascending order.
• Take $k_1,k_2,\\dots,k_{|A|}$ such that $A=\\lbrace C_{k_1},C_{k_2},\\dots,C_{k_{|A|}}\\rbrace$. Then, let $\\displaystyle f(A,B)=\\sum_{i=1}^{|A|} k_i$.

For example, if $A=\\lbrace 1,3\\rbrace$ and $B=\\lbrace 2,8\\rbrace$, then $C=(1,2,3,8)$, so $A=\\lbrace C_1,C_3\\rbrace$; thus, $f(A,B)=1+3=4$.

We have $N$ sets of integers, $S_1,S_2\\dots,S_N$, each of which has $M$ elements. For each $i\\ (1 \\leq i \\leq N)$, $S_i = \\lbrace A_{i,1},A_{i,2},\\dots,A_{i,M}\\rbrace$. Here, it is guaranteed that $S_i \\cap S_j = \\emptyset\\ (i \\neq j)$.

Find $\\displaystyle \\sum_{1\\leq i<j \\leq N} f(S_i, S_j)$.

Constraints

• $1\\leq N \\leq 10^4$
• $1\\leq M \\leq 10^2$
• $1\\leq A_{i,j} \\leq 10^9$
• If $i_1 \\neq i_2$ or $j_1 \\neq j_2$, then $A_{i_1,j_1} \\neq A_{i_2,j_2}$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$ $A_{1,1}$ $A_{1,2}$ $\\dots$ $A_{1,M}$ $\\vdots$ $A_{N,1}$ $A_{N,2}$ $\\dots$ $A_{N,M}$

Output

Print the answer as an integer.

Sample Input 1

3 2
1 3
2 8
4 6

Sample Output 1

12

$S_1$ and $S_2$ respectively coincide with $A$ and $B$ exemplified in the problem statement, and $f(S_1,S_2)=1+3=4$. Since $f(S_1,S_3)=1+2=3$ and $f(S_2,S_3)=1+4=5$, the answer is $4+3+5=12$.

Sample Input 2

1 1
306

Sample Output 2

0

Sample Input 3

4 4
155374934 164163676 576823355 954291757
797829355 404011431 353195922 138996221
191890310 782177068 818008580 384836991
160449218 545531545 840594328 501899080

Sample Output 3

102