I already assigned 36 teams into an array of 144 match-ups, each facing off against eight opponents. I want to divide the matchups into 8 rounds, so it has 18 matches per round, but the constraint is that each team can only compete once per round. It's basically the new UEFA Champion League Swiss system format. I have tried a while loop to keep retrying and shuffling the matchup but after 100 trials it still doesn't work. Some rounds have fewer or more than 18 matches. Do you think it is possible without changing the matchups? Here's my code [jsFiddle]:
const matchups = [
[
"26",
"10"
],
[
"26",
"23"
],
[
"26",
"7"
],
[
"28",
"26"
],
[
"21",
"26"
],
[
"32",
"26"
],
[
"36",
"26"
],
[
"26",
"22"
],
[
"43",
"25"
],
[
"25",
"54"
],
[
"25",
"11"
],
[
"37",
"25"
],
[
"16",
"25"
],
[
"27",
"25"
],
[
"25",
"20"
],
[
"25",
"2"
],
[
"14",
"36"
],
[
"37",
"36"
],
[
"36",
"43"
],
[
"36",
"15"
],
[
"11",
"36"
],
[
"29",
"36"
],
[
"36",
"41"
],
[
"23",
"3"
],
[
"23",
"24"
],
[
"23",
"43"
],
[
"27",
"23"
],
[
"10",
"23"
],
[
"29",
"23"
],
[
"23",
"37"
],
[
"54",
"13"
],
[
"48",
"54"
],
[
"54",
"40"
],
[
"54",
"41"
],
[
"54",
"18"
],
[
"34",
"54"
],
[
"12",
"54"
],
[
"2",
"29"
],
[
"2",
"12"
],
[
"24",
"2"
],
[
"2",
"13"
],
[
"7",
"2"
],
[
"20",
"2"
],
[
"2",
"21"
],
[
"7",
"43"
],
[
"1",
"43"
],
[
"43",
"15"
],
[
"43",
"41"
],
[
"43",
"28"
],
[
"48",
"37"
],
[
"7",
"37"
],
[
"22",
"37"
],
[
"37",
"11"
],
[
"37",
"24"
],
[
"1",
"27"
],
[
"11",
"1"
],
[
"1",
"12"
],
[
"14",
"1"
],
[
"1",
"21"
],
[
"9",
"1"
],
[
"29",
"1"
],
[
"35",
"16"
],
[
"35",
"20"
],
[
"10",
"35"
],
[
"28",
"35"
],
[
"35",
"19"
],
[
"11",
"35"
],
[
"22",
"35"
],
[
"35",
"48"
],
[
"15",
"33"
],
[
"17",
"15"
],
[
"15",
"40"
],
[
"15",
"10"
],
[
"12",
"15"
],
[
"15",
"9"
],
[
"33",
"11"
],
[
"9",
"11"
],
[
"11",
"34"
],
[
"27",
"19"
],
[
"48",
"27"
],
[
"34",
"27"
],
[
"13",
"27"
],
[
"27",
"33"
],
[
"9",
"48"
],
[
"9",
"17"
],
[
"28",
"9"
],
[
"20",
"9"
],
[
"14",
"9"
],
[
"17",
"14"
],
[
"28",
"17"
],
[
"17",
"48"
],
[
"17",
"20"
],
[
"16",
"17"
],
[
"22",
"17"
],
[
"19",
"3"
],
[
"19",
"40"
],
[
"13",
"19"
],
[
"19",
"22"
],
[
"19",
"29"
],
[
"33",
"19"
],
[
"32",
"21"
],
[
"10",
"32"
],
[
"18",
"32"
],
[
"32",
"28"
],
[
"16",
"32"
],
[
"32",
"3"
],
[
"20",
"32"
],
[
"22",
"28"
],
[
"13",
"22"
],
[
"10",
"22"
],
[
"41",
"14"
],
[
"41",
"7"
],
[
"41",
"29"
],
[
"41",
"34"
],
[
"16",
"41"
],
[
"3",
"16"
],
[
"3",
"28"
],
[
"3",
"10"
],
[
"3",
"7"
],
[
"24",
"3"
],
[
"18",
"16"
],
[
"13",
"16"
],
[
"18",
"7"
],
[
"7",
"14"
],
[
"33",
"29"
],
[
"29",
"34"
],
[
"21",
"13"
],
[
"21",
"33"
],
[
"21",
"12"
],
[
"24",
"21"
],
[
"20",
"48"
],
[
"48",
"10"
],
[
"40",
"14"
],
[
"24",
"40"
],
[
"40",
"12"
],
[
"40",
"18"
],
[
"40",
"34"
],
[
"12",
"18"
],
[
"12",
"20"
],
[
"34",
"13"
],
[
"34",
"18"
],
[
"14",
"24"
],
[
"18",
"33"
],
[
"33",
"24"
]
]
const totalRounds = 8
const matchesEachRound = 18;
let rounds: TeamId[][][] = [];
let trial = 0;
while (trial++ < 100) {
rounds = Array(totalRounds)
.fill([])
.map(() => []);
for (const matchup of _.shuffle(matchups)) {
let findTargetRound = rounds.find((round) => {
return (
(round.length < matchesEachRound &&
// both teams not complete in this round
_.intersection(round.flat(), matchup).length === 0)
);
});
if (findTargetRound) {
findTargetRound.push(matchup);
}
}
if (rounds.flat().length === matchups.length) {
break;
}
}
console.log(rounds)
Solution below. I found this by converting your problem to a graph, where each match is a node, and each pair of matches gets an edge if they're compatible, meaning none of the teams involved is the same.
Then, I used a probabilistic clique-finding technique called "iterated greedy" to find a set of a cliques of size 18 in this graph. Finally, I translated that back to the sets of matches.
I didn't count the iterations it took, but it was a large number, hundreds of millions if not billions. I ran the algorithm again and counted iterations -- the second time it clocked in at 1.7 billion.
First, I'll number your matches, for convenience:
0: match between 26 and 10, [26, 10]
1: match between 26 and 23, [26, 23]
2: match between 26 and 7, [26, 7]
3: match between 28 and 26, [28, 26]
4: match between 21 and 26, [21, 26]
5: match between 32 and 26, [32, 26]
6: match between 36 and 26, [36, 26]
7: match between 26 and 22, [26, 22]
8: match between 43 and 25, [43, 25]
9: match between 25 and 54, [25, 54]
10: match between 25 and 11, [25, 11]
11: match between 37 and 25, [37, 25]
12: match between 16 and 25, [16, 25]
13: match between 27 and 25, [27, 25]
14: match between 25 and 20, [25, 20]
15: match between 25 and 2, [25, 2]
16: match between 14 and 36, [14, 36]
17: match between 37 and 36, [37, 36]
18: match between 36 and 43, [36, 43]
19: match between 36 and 15, [36, 15]
20: match between 11 and 36, [11, 36]
21: match between 29 and 36, [29, 36]
22: match between 36 and 41, [36, 41]
23: match between 23 and 3, [23, 3]
24: match between 23 and 24, [23, 24]
25: match between 23 and 43, [23, 43]
26: match between 27 and 23, [27, 23]
27: match between 10 and 23, [10, 23]
28: match between 29 and 23, [29, 23]
29: match between 23 and 37, [23, 37]
30: match between 54 and 13, [54, 13]
31: match between 48 and 54, [48, 54]
32: match between 54 and 40, [54, 40]
33: match between 54 and 41, [54, 41]
34: match between 54 and 18, [54, 18]
35: match between 34 and 54, [34, 54]
36: match between 12 and 54, [12, 54]
37: match between 2 and 29, [2, 29]
38: match between 2 and 12, [2, 12]
39: match between 24 and 2, [24, 2]
40: match between 2 and 13, [2, 13]
41: match between 7 and 2, [7, 2]
42: match between 20 and 2, [20, 2]
43: match between 2 and 21, [2, 21]
44: match between 7 and 43, [7, 43]
45: match between 1 and 43, [1, 43]
46: match between 43 and 15, [43, 15]
47: match between 43 and 41, [43, 41]
48: match between 43 and 28, [43, 28]
49: match between 48 and 37, [48, 37]
50: match between 7 and 37, [7, 37]
51: match between 22 and 37, [22, 37]
52: match between 37 and 11, [37, 11]
53: match between 37 and 24, [37, 24]
54: match between 1 and 27, [1, 27]
55: match between 11 and 1, [11, 1]
56: match between 1 and 12, [1, 12]
57: match between 14 and 1, [14, 1]
58: match between 1 and 21, [1, 21]
59: match between 9 and 1, [9, 1]
60: match between 29 and 1, [29, 1]
61: match between 35 and 16, [35, 16]
62: match between 35 and 20, [35, 20]
63: match between 10 and 35, [10, 35]
64: match between 28 and 35, [28, 35]
65: match between 35 and 19, [35, 19]
66: match between 11 and 35, [11, 35]
67: match between 22 and 35, [22, 35]
68: match between 35 and 48, [35, 48]
69: match between 15 and 33, [15, 33]
70: match between 17 and 15, [17, 15]
71: match between 15 and 40, [15, 40]
72: match between 15 and 10, [15, 10]
73: match between 12 and 15, [12, 15]
74: match between 15 and 9, [15, 9]
75: match between 33 and 11, [33, 11]
76: match between 9 and 11, [9, 11]
77: match between 11 and 34, [11, 34]
78: match between 27 and 19, [27, 19]
79: match between 48 and 27, [48, 27]
80: match between 34 and 27, [34, 27]
81: match between 13 and 27, [13, 27]
82: match between 27 and 33, [27, 33]
83: match between 9 and 48, [9, 48]
84: match between 9 and 17, [9, 17]
85: match between 28 and 9, [28, 9]
86: match between 20 and 9, [20, 9]
87: match between 14 and 9, [14, 9]
88: match between 17 and 14, [17, 14]
89: match between 28 and 17, [28, 17]
90: match between 17 and 48, [17, 48]
91: match between 17 and 20, [17, 20]
92: match between 16 and 17, [16, 17]
93: match between 22 and 17, [22, 17]
94: match between 19 and 3, [19, 3]
95: match between 19 and 40, [19, 40]
96: match between 13 and 19, [13, 19]
97: match between 19 and 22, [19, 22]
98: match between 19 and 29, [19, 29]
99: match between 33 and 19, [33, 19]
100: match between 32 and 21, [32, 21]
101: match between 10 and 32, [10, 32]
102: match between 18 and 32, [18, 32]
103: match between 32 and 28, [32, 28]
104: match between 16 and 32, [16, 32]
105: match between 32 and 3, [32, 3]
106: match between 20 and 32, [20, 32]
107: match between 22 and 28, [22, 28]
108: match between 13 and 22, [13, 22]
109: match between 10 and 22, [10, 22]
110: match between 41 and 14, [41, 14]
111: match between 41 and 7, [41, 7]
112: match between 41 and 29, [41, 29]
113: match between 41 and 34, [41, 34]
114: match between 16 and 41, [16, 41]
115: match between 3 and 16, [3, 16]
116: match between 3 and 28, [3, 28]
117: match between 3 and 10, [3, 10]
118: match between 3 and 7, [3, 7]
119: match between 24 and 3, [24, 3]
120: match between 18 and 16, [18, 16]
121: match between 13 and 16, [13, 16]
122: match between 18 and 7, [18, 7]
123: match between 7 and 14, [7, 14]
124: match between 33 and 29, [33, 29]
125: match between 29 and 34, [29, 34]
126: match between 21 and 13, [21, 13]
127: match between 21 and 33, [21, 33]
128: match between 21 and 12, [21, 12]
129: match between 24 and 21, [24, 21]
130: match between 20 and 48, [20, 48]
131: match between 48 and 10, [48, 10]
132: match between 40 and 14, [40, 14]
133: match between 24 and 40, [24, 40]
134: match between 40 and 12, [40, 12]
135: match between 40 and 18, [40, 18]
136: match between 40 and 34, [40, 34]
137: match between 12 and 18, [12, 18]
138: match between 12 and 20, [12, 20]
139: match between 34 and 13, [34, 13]
140: match between 34 and 18, [34, 18]
141: match between 14 and 24, [14, 24]
142: match between 18 and 33, [18, 33]
143: match between 33 and 24, [33, 24]
Group 1:
4: match between 21 and 26, [21, 26]
11: match between 37 and 25, [37, 25]
20: match between 11 and 36, [11, 36]
25: match between 23 and 43, [23, 43]
33: match between 54 and 41, [54, 41]
37: match between 2 and 29, [2, 29]
56: match between 1 and 12, [1, 12]
64: match between 28 and 35, [28, 35]
69: match between 15 and 33, [15, 33]
78: match between 27 and 19, [27, 19]
84: match between 9 and 17, [9, 17]
105: match between 32 and 3, [32, 3]
109: match between 10 and 22, [10, 22]
120: match between 18 and 16, [18, 16]
123: match between 7 and 14, [7, 14]
130: match between 20 and 48, [20, 48]
133: match between 24 and 40, [24, 40]
139: match between 34 and 13, [34, 13]
Group 2
2: match between 26 and 7, [26, 7]
10: match between 25 and 11, [25, 11]
16: match between 14 and 36, [14, 36]
24: match between 23 and 24, [23, 24]
32: match between 54 and 40, [54, 40]
42: match between 20 and 2, [20, 2]
48: match between 43 and 28, [43, 28]
49: match between 48 and 37, [48, 37]
54: match between 1 and 27, [1, 27]
63: match between 10 and 35, [10, 35]
74: match between 15 and 9, [15, 9]
93: match between 22 and 17, [22, 17]
94: match between 19 and 3, [19, 3]
102: match between 18 and 32, [18, 32]
113: match between 41 and 34, [41, 34]
121: match between 13 and 16, [13, 16]
124: match between 33 and 29, [33, 29]
128: match between 21 and 12, [21, 12]
Group 3:
7: match between 26 and 22, [26, 22]
8: match between 43 and 25, [43, 25]
17: match between 37 and 36, [37, 36]
28: match between 29 and 23, [29, 23]
30: match between 54 and 13, [54, 13]
39: match between 24 and 2, [24, 2]
55: match between 11 and 1, [11, 1]
65: match between 35 and 19, [35, 19]
71: match between 15 and 40, [15, 40]
79: match between 48 and 27, [48, 27]
87: match between 14 and 9, [14, 9]
92: match between 16 and 17, [16, 17]
103: match between 32 and 28, [32, 28]
111: match between 41 and 7, [41, 7]
117: match between 3 and 10, [3, 10]
127: match between 21 and 33, [21, 33]
138: match between 12 and 20, [12, 20]
140: match between 34 and 18, [34, 18]
Group 4:
1: match between 26 and 23, [26, 23]
9: match between 25 and 54, [25, 54]
22: match between 36 and 41, [36, 41]
43: match between 2 and 21, [2, 21]
44: match between 7 and 43, [7, 43]
51: match between 22 and 37, [22, 37]
60: match between 29 and 1, [29, 1]
66: match between 11 and 35, [11, 35]
73: match between 12 and 15, [12, 15]
80: match between 34 and 27, [34, 27]
85: match between 28 and 9, [28, 9]
88: match between 17 and 14, [17, 14]
96: match between 13 and 19, [13, 19]
106: match between 20 and 32, [20, 32]
115: match between 3 and 16, [3, 16]
131: match between 48 and 10, [48, 10]
135: match between 40 and 18, [40, 18]
143: match between 33 and 24, [33, 24]
Group 5:
3: match between 28 and 26, [28, 26]
15: match between 25 and 2, [25, 2]
21: match between 29 and 36, [29, 36]
29: match between 23 and 37, [23, 37]
34: match between 54 and 18, [54, 18]
45: match between 1 and 43, [1, 43]
67: match between 22 and 35, [22, 35]
72: match between 15 and 10, [15, 10]
77: match between 11 and 34, [11, 34]
81: match between 13 and 27, [13, 27]
83: match between 9 and 48, [9, 48]
91: match between 17 and 20, [17, 20]
99: match between 33 and 19, [33, 19]
104: match between 16 and 32, [16, 32]
110: match between 41 and 14, [41, 14]
118: match between 3 and 7, [3, 7]
129: match between 24 and 21, [24, 21]
134: match between 40 and 12, [40, 12]
Group 6:
5: match between 32 and 26, [32, 26]
13: match between 27 and 25, [27, 25]
18: match between 36 and 43, [36, 43]
27: match between 10 and 23, [10, 23]
35: match between 34 and 54, [34, 54]
41: match between 7 and 2, [7, 2]
53: match between 37 and 24, [37, 24]
58: match between 1 and 21, [1, 21]
68: match between 35 and 48, [35, 48]
70: match between 17 and 15, [17, 15]
75: match between 33 and 11, [33, 11]
86: match between 20 and 9, [20, 9]
98: match between 19 and 29, [19, 29]
108: match between 13 and 22, [13, 22]
114: match between 16 and 41, [16, 41]
116: match between 3 and 28, [3, 28]
132: match between 40 and 14, [40, 14]
137: match between 12 and 18, [12, 18]
Group 7:
0: match between 26 and 10, [26, 10]
12: match between 16 and 25, [16, 25]
19: match between 36 and 15, [36, 15]
23: match between 23 and 3, [23, 3]
36: match between 12 and 54, [12, 54]
40: match between 2 and 13, [2, 13]
47: match between 43 and 41, [43, 41]
52: match between 37 and 11, [37, 11]
59: match between 9 and 1, [9, 1]
62: match between 35 and 20, [35, 20]
82: match between 27 and 33, [27, 33]
90: match between 17 and 48, [17, 48]
95: match between 19 and 40, [19, 40]
100: match between 32 and 21, [32, 21]
107: match between 22 and 28, [22, 28]
122: match between 18 and 7, [18, 7]
125: match between 29 and 34, [29, 34]
141: match between 14 and 24, [14, 24]
Group 8:
6: match between 36 and 26, [36, 26]
14: match between 25 and 20, [25, 20]
26: match between 27 and 23, [27, 23]
31: match between 48 and 54, [48, 54]
38: match between 2 and 12, [2, 12]
46: match between 43 and 15, [43, 15]
50: match between 7 and 37, [7, 37]
57: match between 14 and 1, [14, 1]
61: match between 35 and 16, [35, 16]
76: match between 9 and 11, [9, 11]
89: match between 28 and 17, [28, 17]
97: match between 19 and 22, [19, 22]
101: match between 10 and 32, [10, 32]
112: match between 41 and 29, [41, 29]
119: match between 24 and 3, [24, 3]
126: match between 21 and 13, [21, 13]
136: match between 40 and 34, [40, 34]
142: match between 18 and 33, [18, 33]
Note, I was careful to transcribe the groupings above correctly, but it's not the raw output of my code, which is hard to interpret. I'll put it here for the record, and explain how to read it.
Each of the 8 rows below represents a clique, where members are represented by the larger squares, and nonmembers by the dots. The indices of the dots and squares are identical to the ids I gave your matches. E.g., in the first row, the squares at indices 6 and 14 (0-indexed) indicate that matches 6 & 14 belong to this grouping.
⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝ 18
▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝ 18
⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝ 18
⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝▪⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝ 18
⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪ 18
⬝⬝⬝⬝⬝⬝⬝▪▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝▪⬝⬝⬝ 18
⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝ 18
⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝⬝▪⬝⬝⬝⬝⬝⬝⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝⬝⬝⬝▪⬝⬝▪⬝⬝⬝⬝⬝▪⬝⬝⬝⬝ 18