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

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.

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.

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

见题面 Input 部分

见题面 Output 部分