## Saturday, August 17, 2013

### Exploiting exponential curve

http://www.scilogs.com/the_science_talent_project/my-simple-spaced-repetition-system/ says that we should repeat material with exponentially decreasing rate. I have estimated that this allows you to add a new item to learn every time unit to fill the gaps of free slots that appear over time. I've guessed that, provided the exponent of 2, this allows to introduce a new item every second clock. However, the simulation shows otherwise

public class ExponentialLearning {

public static void main(String[] args) {
int densityCounter = 0;
int runtime = 200;//10000;
final int shift = 2; // introduce a new item every n cycles
int shiftNext = 0;

class Item {
final int what;
int when; // when next ouput
Item(int what, int time) {
this.what = what;
this.when = 1;
//System.out.print("(" + this + " created) ");
}

public String toString() {
return what + "@" + when;
}
}

Collection counters = new ArrayList<>();

for (int time = 0, exponent = 1, exponentNext; time != runtime ; time++) {

System.out.print(time + ": ");

// add new item every shift cycles
if (time == shiftNext) {
shiftNext += shift;
}

exponentNext = exponent * 2;
for (Item item : counters) {
if (item.when + item.what*shift == time) {
//System.out.print(", output: " + item.what + " ");
item.when *= 2;
}
}

exponent = exponentNext;

if (!output.isEmpty()) {
for (Integer integer : output) {
System.out.print(integer + ", ");
densityCounter++;
}
output.removeFirst();

}

System.out.println();
}

System.out.println("average density = " + ((float)densityCounter / (float)runtime));
}
}

The curve below shows the output: you see exponentially accumulating amount of material to reherse (horizontally) at every next time step (vertically).

1: 1,
2: 1,
3: 2,
4: 2, 1,
5: 3, 1,
6: 3, 2, 1,
7: 4, 2, 1,
8: 4, 3, 1, 2, 1,
9: 5, 3, 1, 2, 1,
10: 5, 4, 2, 3, 1, 2, 1,
11: 6, 4, 2, 3, 1, 2, 1,
12: 6, 5, 3, 4, 2, 3, 1, 2, 1,
13: 7, 5, 3, 4, 2, 3, 1, 2, 1,
14: 7, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
15: 8, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
16: 8, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
17: 9, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
18: 9, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
19: 10, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
20: 10, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
21: 11, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
22: 11, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
23: 12, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
24: 12, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
25: 13, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
26: 13, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
27: 14, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
28: 14, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
29: 15, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
30: 15, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
31: 16, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
32: 16, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
33: 17, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
34: 17, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
35: 18, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
36: 18, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
37: 19, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
38: 19, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
39: 20, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
40: 20, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
41: 21, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
42: 21, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
43: 22, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
44: 22, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
45: 23, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
46: 23, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
47: 24, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
48: 24, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
49: 25, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
50: 25, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
51: 26, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
52: 26, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
53: 27, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
54: 27, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
55: 28, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
56: 28, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
57: 29, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
58: 29, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
59: 30, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
60: 30, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
61: 31, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
62: 31, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
63: 32, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
64: 32, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
65: 33, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
66: 33, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
67: 34, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
68: 34, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
69: 35, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
70: 35, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
71: 36, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
72: 36, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
73: 37, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
74: 37, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
75: 38, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
76: 38, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
77: 39, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
78: 39, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
79: 40, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
80: 40, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
81: 41, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
82: 41, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
83: 42, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
84: 42, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
85: 43, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
86: 43, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
87: 44, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
88: 44, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
89: 45, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
90: 45, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
91: 46, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
92: 46, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
93: 47, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
94: 47, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
95: 48, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
96: 48, 47, 45, 41, 33, 17, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
97: 49, 47, 45, 41, 33, 17, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
98: 49, 48, 46, 42, 34, 18, 47, 45, 41, 33, 17, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,
99: 50, 48, 46, 42, 34, 18, 47, 45, 41, 33, 17, 46, 44, 40, 32, 16, 45, 43, 39, 31, 15, 44, 42, 38, 30, 14, 43, 41, 37, 29, 13, 42, 40, 36, 28, 12, 41, 39, 35, 27, 11, 40, 38, 34, 26, 10, 39, 37, 33, 25, 9, 38, 36, 32, 24, 8, 37, 35, 31, 23, 7, 36, 34, 30, 22, 6, 35, 33, 29, 21, 5, 34, 32, 28, 20, 4, 33, 31, 27, 19, 3, 32, 30, 26, 18, 2, 31, 29, 25, 17, 1, 30, 28, 24, 16, 29, 27, 23, 15, 28, 26, 22, 14, 27, 25, 21, 13, 26, 24, 20, 12, 25, 23, 19, 11, 24, 22, 18, 10, 23, 21, 17, 9, 22, 20, 16, 8, 21, 19, 15, 7, 20, 18, 14, 6, 19, 17, 13, 5, 18, 16, 12, 4, 17, 15, 11, 3, 16, 14, 10, 2, 15, 13, 9, 1, 14, 12, 8, 13, 11, 7, 12, 10, 6, 11, 9, 5, 10, 8, 4, 9, 7, 3, 8, 6, 2, 7, 5, 1, 6, 4, 5, 3, 4, 2, 3, 1, 2, 1,



average density = 79 items/iteration