You are given $n$ integers. You need to choose a subset and put the chosen numbers in a beautiful rectangle (rectangular matrix). Each chosen number should occupy one of its rectangle cells, each cell must be filled with exactly one chosen number. Some of the $n$ numbers may not be chosen.

A rectangle (rectangular matrix) is called beautiful if in each row and in each column all values are different.

What is the largest (by the total number of cells) beautiful rectangle you can construct? Print the rectangle itself.


-----Input-----

The first line contains $n$ ($1 \le n \le 4\cdot10^5$). The second line contains $n$ integers ($1 \le a_i \le 10^9$).


-----Output-----

In the first line print $x$ ($1 \le x \le n$) — the total number of cells of the required maximum beautiful rectangle. In the second line print $p$ and $q$ ($p \cdot q=x$): its sizes. In the next $p$ lines print the required rectangle itself. If there are several answers, print any.


-----Examples-----
Input
12
3 1 4 1 5 9 2 6 5 3 5 8

Output
12
3 4
1 2 3 5
3 1 5 4
5 6 8 9

Input
5
1 1 1 1 1

Output
1
1 1
1

Difficulty: competition

Starter code:

Solutions:

from collections import Counter
from itertools import accumulate
from math import sqrt
from operator import itemgetter
import sys
 
n = int(input())
cnt = Counter(map(int, input().split()))
nums, counts = zip(*sorted(cnt.items(), key=itemgetter(1)))
acc = [0] + list(accumulate(counts))
area = 1
h, w = 1, 1
i = len(counts)
 
for y in range(int(sqrt(n)), 0, -1):
    while i and counts[i-1] > y:
        i -= 1
    total = acc[i] + (len(counts) - i) * y
    x = total // y
    if y <= x and area < x * y:
        h, w, area = y, x, x*y
 
ans = [[0]*w for _ in range(h)]
i = len(counts)-1
num, count = nums[i], min(h, counts[i])
 
for x in range(w):
    for y in range(h):
        ans[y][(x + y) % w] = num
 
        count -= 1
        if count == 0:
            i -= 1
            num, count = nums[i], h if h < counts[i] else counts[i]
 
print(area)
print(h, w)
for y in range(h):
    sys.stdout.write(' '.join(map(str, ans[y])) + '\n')

import sys
input = sys.stdin.readline
 
n=int(input())
A=list(map(int,input().split()))

from collections import Counter
 
C=Counter(A)

import math

MAXV=max(max(C.values()),int(math.sqrt(n)))
 
VCOUNT=[0]*(MAXV+1)
 
for v in list(C.values()):
    VCOUNT[v]+=1
    
SUM=n
 
from itertools import accumulate
 
ACC=list(accumulate(VCOUNT[::-1]))[::-1]
 
 
ANS=0
 
for i in range(MAXV,0,-1):
    if SUM//i>=i:
        if ANS<i*(SUM//i):
            ANS=i*(SUM//i)
            ANSX=i,(SUM//i)
 
    SUM-=ACC[i]
 
print(ANS)
 
X,Y=ANSX[0],ANSX[1]
print(X,Y)
 
A=[[0]*Y for i in range(X)]
 
i=0
j=0
nowj=0
colored=0
same=0
LIST=list(C.most_common())
ind=0
 
while colored<ANS:
    A[i][j],MAX=LIST[ind]
    colored+=1
    i+=1
    j=(j+1)%Y
    if i==X:
        i=0
        nowj+=1
        j=nowj
    same+=1
 
    if same==min(X,MAX):
        ind+=1
        same=0
 
for a in A:
    sys.stdout.write(" ".join(map(str,a))+"\n")


from collections import Counter
from itertools import accumulate
from math import sqrt
from operator import itemgetter
import sys
 
n = int(input())
cnt = Counter(map(int, input().split()))
nums, counts = zip(*sorted(cnt.items(), key=itemgetter(1)))
acc = [0] + list(accumulate(counts))
area = 1
h, w = 1, 1
i = len(counts)
 
for y in range(int(sqrt(n)), 0, -1):
    while i and counts[i-1] > y:
        i -= 1
    total = acc[i] + (len(counts) - i) * y
    x = total // y
    if y <= x and area < x * y:
        h, w, area = y, x, x*y
 
ans = [[0]*w for _ in range(h)]
i = len(counts)-1
num, count = nums[i], min(h, counts[i])
 
for x in range(w):
    for y in range(h):
        ans[y][(x + y) % w] = num
 
        count -= 1
        if count == 0:
            i -= 1
            num, count = nums[i], h if h < counts[i] else counts[i]
 
print(area)
print(h, w)
for y in range(h):
    sys.stdout.write(' '.join(map(str, ans[y])) + '\n')