From ac39ef540a2a52a23e9e0b1aaeb34367e7ac90c1 Mon Sep 17 00:00:00 2001
From: Aaro Koivukangas <aaro.koivukangas@gmail.com>
Date: Thu, 26 Mar 2026 17:03:42 +0200
Subject: [PATCH] Did weeks 10-12

---
 viikko10/allsteps.py       |  39 +++++++++++++
 viikko10/coinsum.py        |  24 ++++++++
 viikko10/countlis.py       |  23 ++++++++
 viikko10/findlis.py        |  31 ++++++++++
 viikko10/formula.py        |  52 +++++++++++++++++
 viikko10/machine.py        |  25 ++++++++
 viikko11/fliplist.py       |  46 +++++++++++++++
 viikko11/fliptwo.py        |  21 +++++++
 viikko11/smallest_tenth.py |  38 +++++++++++++
 viikko11/stack.py          |  24 ++++++++
 viikko11/tasklist.py       |  12 ++++
 viikko12/minmax.py         |  65 +++++++++++++++++++++
 viikko12/prevnext.py       | 114 +++++++++++++++++++++++++++++++++++++
 viikko12/treeheight.py     |  64 +++++++++++++++++++++
 viikko12/treeremove.py     |  67 ++++++++++++++++++++++
 viikko12/treesize.py       |  50 ++++++++++++++++
 16 files changed, 695 insertions(+)
 create mode 100644 viikko10/allsteps.py
 create mode 100644 viikko10/coinsum.py
 create mode 100644 viikko10/countlis.py
 create mode 100644 viikko10/findlis.py
 create mode 100644 viikko10/formula.py
 create mode 100644 viikko10/machine.py
 create mode 100644 viikko11/fliplist.py
 create mode 100644 viikko11/fliptwo.py
 create mode 100644 viikko11/smallest_tenth.py
 create mode 100644 viikko11/stack.py
 create mode 100644 viikko11/tasklist.py
 create mode 100644 viikko12/minmax.py
 create mode 100644 viikko12/prevnext.py
 create mode 100644 viikko12/treeheight.py
 create mode 100644 viikko12/treeremove.py
 create mode 100644 viikko12/treesize.py

diff --git a/viikko10/allsteps.py b/viikko10/allsteps.py
new file mode 100644
index 0000000..025bf1c
--- /dev/null
+++ b/viikko10/allsteps.py
@@ -0,0 +1,39 @@
+import math
+
+
+def min_steps(x):
+    result = {}
+    result[1] = 0
+
+    for i in range(1, x + 1):
+        if result.get(i, -1) >= 0:
+            result[i + 3] = min(result.get(i + 3, math.inf), result[i] + 1)
+            result[i * 2] = min(result.get(i * 2, math.inf), result[i] + 1)
+            # print(f"i: {i}, curr: {result[i]}, +3 => {result[i+3]}, *2 => {result[i*2]}", x)
+
+    print(result.get(x, -1))
+    return result.get(x, -1)
+
+
+def count_steps(x):
+    result = {}
+    result[1] = 1
+
+    for i in range(1, x + 1):
+        result[i + 3] = result.get(i + 3, 0) + result.get(i, 0)
+        result[i * 2] = result.get(i * 2, 0) + result.get(i, 0)
+
+    print("Result:", result.get(x, 0), x)
+    return result.get(x, 0)
+
+
+if __name__ == "__main__":
+    assert count_steps(1) == 1
+    assert count_steps(2) == 1
+    assert count_steps(3) == 0
+    assert count_steps(4) == 2
+    assert count_steps(5) == 1
+    assert count_steps(17) == 5
+    assert count_steps(42) == 0
+    assert count_steps(100) == 242
+    assert count_steps(1000) == 2948311
diff --git a/viikko10/coinsum.py b/viikko10/coinsum.py
new file mode 100644
index 0000000..bd8d9f7
--- /dev/null
+++ b/viikko10/coinsum.py
@@ -0,0 +1,24 @@
+def can_create(coins, target):
+    result = {}
+    for x in range(target + 1):
+        result[x] = True if x in coins else False
+
+    for i in range(1, target + 1):
+        for c in coins:
+            if i - c >= 0 and not result.get(i + c):
+                result[i + c] = True if result[i] or c == i else False
+                # print(f"Calc: {i:2} +{c:2} = {i+c:2} => {result[i+c]}, because previous {i-c} = {result[i-c]}")
+
+    print("RESULT:", result[target])
+    return result[target]
+
+
+if __name__ == "__main__":
+    assert can_create([1], 1)
+    assert can_create([1, 2, 5], 13)
+    assert not can_create([2, 4, 6], 13)
+    assert can_create([1], 42)
+    assert can_create([2, 4, 6], 42)
+    assert not can_create([3], 1337)
+    assert can_create([3, 4], 1337)
+    assert can_create([3, 7, 9], 16)
diff --git a/viikko10/countlis.py b/viikko10/countlis.py
new file mode 100644
index 0000000..e716de0
--- /dev/null
+++ b/viikko10/countlis.py
@@ -0,0 +1,23 @@
+def count_sequences(numbers):
+    result = {}
+    len_result = {}
+
+    max_len = 0
+    for i in range(len(numbers)):
+        result[i] = 1
+        for j in range(i):
+            if numbers[j] < numbers[i]:
+                result[i] = max(result[i], result[j] + 1)
+        max_len = max(max_len, result[i])
+        len_result[result[i]] = len_result.get(result[i], 0) + 1
+
+    return len_result[max_len]
+
+if __name__ == "__main__":
+    print(count_sequences([1, 2, 3])) # 1
+    print(count_sequences([3, 2, 1])) # 3
+    print(count_sequences([1, 1, 1, 1, 1])) # 5
+
+    print(count_sequences([1, 8, 2, 7, 3, 6])) # 1
+    print(count_sequences([1, 1, 2, 2, 3, 3])) # 8
+    print(count_sequences([4, 1, 5, 6, 3, 4, 3, 8])) # 3
diff --git a/viikko10/findlis.py b/viikko10/findlis.py
new file mode 100644
index 0000000..a7eaad3
--- /dev/null
+++ b/viikko10/findlis.py
@@ -0,0 +1,31 @@
+def find_sequence(numbers):
+    result = {}
+    for i in range(len(numbers)):
+        num = numbers[i]
+        result[num] = result.get(num, [num])
+
+        for key in result.keys():
+            if key < num:
+                result[num] = result[key] + [num] if len(result[num]) <= len(result[key]) + 1 else result[num]
+
+    longest = sorted(list(result.values()), key=len, reverse=True)
+    # print(longest)
+    # print()
+    return longest[0]
+            
+
+
+if __name__ == "__main__":
+    assert find_sequence([1, 2, 3]) == [1, 2, 3]
+    assert find_sequence([3, 2, 1]) == [3]
+    assert find_sequence([1, 1, 1, 1, 1]) == [1]
+    assert find_sequence([1, 8, 2, 7, 3, 6]) == [1, 2, 3, 6]
+
+    assert find_sequence([1, 1, 2, 2, 3, 3]) == [1, 2, 3]
+    assert find_sequence([4, 1, 5, 6, 3, 4, 3, 8]) == [1, 5, 6, 8]
+    assert find_sequence([9, 2, 9, 1]) == [2, 9]
+    assert find_sequence([8, 6, 1, 1, 9, 4, 7]) == [1, 4, 7]
+    assert find_sequence([10, 34, 43, 17, 33, 83, 73, 35, 92, 68, 33, 14, 13, 80]) == [10, 17, 33, 35, 68 ,80]
+    assert find_sequence([96, 80, 54, 81, 39, 42, 17, 13, 4, 10, 50, 26, 13, 95, 12, 8, 75, 38, 27, 68, 64, 36, 25, 89, 96]) != []
+    assert find_sequence([65, 4, 62, 22, 47, 99, 83, 11, 23, 22, 61, 49, 9, 60, 32, 53, 59, 81, 36, 68, 66, 69, 47, 23, 29, 95, 85, 31, 83, 82, 44, 31, 19, 22, 97, 91, 48, 69, 49]) != []
+    assert find_sequence([79, 26, 75, 65, 34, 29, 33, 73, 13, 10, 29, 43, 78, 8, 25, 9, 78, 28, 70, 58, 86, 87, 52, 7, 1, 81, 62, 44, 49, 15, 6, 14, 94, 37, 90, 61, 28, 39, 10, 72, 80, 95, 91, 65, 99, 60, 54, 68, 84, 76, 70, 54, 65, 54, 8, 37, 57, 87, 85, 32, 10, 44, 47, 5, 91, 17, 88]) != []
diff --git a/viikko10/formula.py b/viikko10/formula.py
new file mode 100644
index 0000000..f7adb98
--- /dev/null
+++ b/viikko10/formula.py
@@ -0,0 +1,52 @@
+from fractions import Fraction
+import decimal
+import math
+from math import factorial
+
+
+def calc_binomial(a: int, b: int) -> int:
+    a_fact = factorial(a)
+    b_fact = factorial(b)
+    a_b_fact = factorial(a - b)
+    denominator = b_fact * a_b_fact
+
+    # This has to be // for some reason...
+    result = a_fact // denominator
+    assert result == math.comb(a, b)
+
+    return result
+
+
+def count_sequences(n: int):
+    if n % 2 != 0:
+        return 0
+
+    n_div = n // 2
+    assert n_div.is_integer()
+
+    binomial = calc_binomial(n, n_div)
+    assert binomial.is_integer()
+
+    # oh man this took time...
+    result_div = Fraction(1, (n_div + 1))
+    result = round(result_div * binomial)
+
+    return int(result)
+
+
+if __name__ == "__main__":
+    assert count_sequences(1) == 0
+    assert count_sequences(2) == 1
+    assert count_sequences(3) == 0
+    assert count_sequences(4) == 2
+    assert count_sequences(5) == 0
+    assert count_sequences(6) == 5
+
+    assert count_sequences(42) == 24466267020
+    assert count_sequences(62) == 14544636039226909
+    assert count_sequences(64) == 55534064877048198
+    assert (
+        count_sequences(1000)
+        == 539497486917039060909410566119711128734834348196703167679426896420410037336371644508208550747509720888947317534973145917768881736628103627844100238921194561723883202123256952806711505149177419849031086149939116975191706558395784192643914160118616272189452807591091542120727401415762287153293056320
+    )
+    assert count_sequences(5000)
diff --git a/viikko10/machine.py b/viikko10/machine.py
new file mode 100644
index 0000000..1a4a550
--- /dev/null
+++ b/viikko10/machine.py
@@ -0,0 +1,25 @@
+import math
+def min_steps(x):
+    result = {}
+    result[1] = 0
+
+    for i in range(1, x + 1):
+        if result.get(i, -1) >= 0:
+            result[i + 3] = min(result.get(i+3, math.inf), result[i] + 1)
+            result[i * 2] = min(result.get(i*2, math.inf), result[i] + 1)
+            # print(f"i: {i}, curr: {result[i]}, +3 => {result[i+3]}, *2 => {result[i*2]}", x)
+
+    print(result.get(x, -1))
+    return result.get(x, -1)
+
+
+if __name__ == "__main__":
+    assert min_steps(1) == 0
+    assert min_steps(2) == 1
+    assert min_steps(3) == -1
+    assert min_steps(4) == 1
+    assert min_steps(5) == 2
+    assert min_steps(17) == 4
+    assert min_steps(42) == -1
+    assert min_steps(100) == 7
+    assert min_steps(1000) == 13
diff --git a/viikko11/fliplist.py b/viikko11/fliplist.py
new file mode 100644
index 0000000..517e1fd
--- /dev/null
+++ b/viikko11/fliplist.py
@@ -0,0 +1,46 @@
+import collections
+
+
+class FlipList:
+    def __init__(self):
+        self.l = collections.deque()
+        self.reverse = False
+
+    def __repr__(self):
+        if self.reverse:
+            return str(list(reversed([x for x in self.l])))
+        else:
+            return str([x for x in self.l])
+
+    def add_first(self, x):
+        if self.reverse:
+            self.l.append(x)
+        else:
+            self.l.appendleft(x)
+
+    def add_last(self, x):
+        if self.reverse:
+            self.l.appendleft(x)
+        else:
+            self.l.append(x)
+
+    def flip(self):
+        self.reverse = not self.reverse
+
+
+if __name__ == "__main__":
+    numbers = FlipList()
+
+    numbers.add_last(1)
+    numbers.add_last(2)
+    numbers.add_last(3)
+    print(numbers)  # [1, 2, 3]
+
+    numbers.add_first(4)
+    print(numbers)  # [4, 1, 2, 3]
+
+    numbers.flip()
+    print(numbers)  # [3, 2, 1, 4]
+
+    numbers.add_last(5)
+    print(numbers)  # [3, 2, 1, 4, 5]
diff --git a/viikko11/fliptwo.py b/viikko11/fliptwo.py
new file mode 100644
index 0000000..34ce63d
--- /dev/null
+++ b/viikko11/fliptwo.py
@@ -0,0 +1,21 @@
+import collections
+
+
+def find_first(size, steps):
+    ls = collections.deque([x for x in range(1, size+1)])
+
+    for i in range(steps):
+        second = ls.popleft()
+        first = ls.popleft()
+
+        ls.append(first)
+        ls.append(second)
+        
+    return ls[0]
+
+if __name__ == "__main__":
+    print(find_first(4, 3)) # 4
+    print(find_first(12, 5)) # 11
+    print(find_first(2, 1000)) # 1
+    print(find_first(99, 555)) # 11
+    print(find_first(12345, 10**6)) # 12295
diff --git a/viikko11/smallest_tenth.py b/viikko11/smallest_tenth.py
new file mode 100644
index 0000000..3ce384d
--- /dev/null
+++ b/viikko11/smallest_tenth.py
@@ -0,0 +1,38 @@
+import time
+import random
+import heapq
+
+
+def smallest_tenth(n):
+    ls = random.choices(range(1, 10**9), k=n)
+
+    start = time.time()
+    ls_sorted = sorted(ls)
+    result1 = sum(ls_sorted[: n // 10])
+    end_sorted = time.time()
+    print("Did sorting")
+
+    ls_heap = []
+    for item in ls:
+        heapq.heappush(ls_heap, item)
+    result2 = sum([heapq.heappop(ls_heap) for _ in range(n // 10)])
+    end_heap_iter = time.time()
+    print("Did heap_iter")
+
+    heapq.heapify(ls)
+    result3 = sum([heapq.heappop(ls) for _ in range(n // 10)])
+    end_heapify = time.time()
+    print("Did heapify")
+
+    print(result1)
+    print(result2)
+    print(result3)
+
+    print(
+        f"Total: {end_heapify - start:.2f}, sorted: {end_sorted - start:.2f}, heap_iter: {end_heap_iter - end_sorted:.2f}, heapify: {end_heapify - end_heap_iter:.2f}"
+    )
+    assert result1 == result2 and result2 == result3
+
+
+if __name__ == "__main__":
+    smallest_tenth(10**7)
diff --git a/viikko11/stack.py b/viikko11/stack.py
new file mode 100644
index 0000000..873c6fe
--- /dev/null
+++ b/viikko11/stack.py
@@ -0,0 +1,24 @@
+import collections
+import time
+
+def stack(n):
+    start = time.time()
+    stack = collections.deque()
+    for x in range(n):
+        stack.append(x)
+
+    add_end = time.time()
+    for x in range(n):
+        stack.popleft()
+
+    end = time.time()
+
+    return f"Total: {end - start:.2f} seconds, to add: {add_end - start:.2f}, to delete: {end - add_end:.2f}"
+
+    
+
+def main():
+    print(stack(10**5))
+
+if __name__ == "__main__":
+    main()
diff --git a/viikko11/tasklist.py b/viikko11/tasklist.py
new file mode 100644
index 0000000..5311020
--- /dev/null
+++ b/viikko11/tasklist.py
@@ -0,0 +1,12 @@
+import heapq
+
+
+class Tasks:
+    def __init__(self):
+        self.t = []
+
+    def add_task(self, name, priority):
+        heapq.heappush(self.t, (-priority, name))
+
+    def fetch_task(self):
+        return heapq.heappop(self.t)[1]
diff --git a/viikko12/minmax.py b/viikko12/minmax.py
new file mode 100644
index 0000000..493baef
--- /dev/null
+++ b/viikko12/minmax.py
@@ -0,0 +1,65 @@
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.left = None
+        self.right = None
+
+class TreeSet:
+    def __init__(self):
+        self.root = None
+
+    def add(self, value):
+        if not self.root:
+            self.root = Node(value)
+            return
+
+        node = self.root
+        while True:
+            if node.value == value:
+                return
+            if node.value > value:
+                if not node.left:
+                    node.left = Node(value)
+                    return
+                node = node.left
+            else:
+                if not node.right:
+                    node.right = Node(value)
+                    return
+                node = node.right
+
+    def min(self):
+        node = self.root
+        while True:
+            if node is None:
+                return None
+            if not node.left:
+                return node.value
+            node = node.left
+
+    def max(self):
+        node = self.root
+        while True:
+            if node is None:
+                return None
+            if not node.right:
+                return node.value
+            node = node.right
+
+if __name__ == "__main__":
+    numbers = TreeSet()
+
+    print(numbers.min()) # None
+    print(numbers.max()) # None
+
+    numbers.add(3)
+    print(numbers.min()) # 3
+    print(numbers.max()) # 3
+
+    numbers.add(4)
+    print(numbers.min()) # 3
+    print(numbers.max()) # 4
+
+    numbers.add(1)
+    print(numbers.min()) # 1
+    print(numbers.max()) # 4
diff --git a/viikko12/prevnext.py b/viikko12/prevnext.py
new file mode 100644
index 0000000..4a521d3
--- /dev/null
+++ b/viikko12/prevnext.py
@@ -0,0 +1,114 @@
+import math
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.left = None
+        self.right = None
+
+    def __repr__(self):
+        return f"({self.value}, l: {self.left}, r: {self.right})"
+
+
+class TreeSet:
+    def __init__(self):
+        self.root = None
+
+    def add(self, value):
+        if not self.root:
+            self.root = Node(value)
+            return
+
+        node = self.root
+        while True:
+            if node.value == value:
+                return
+            if node.value > value:
+                if not node.left:
+                    node.left = Node(value)
+                    return
+                node = node.left
+            else:
+                if not node.right:
+                    node.right = Node(value)
+                    return
+                node = node.right
+
+    def prev(self, value):
+        node = self.root
+
+        if node is None:
+            return None
+
+        highest_lowest = 0
+        while node:
+            print(value, node, highest_lowest)
+            if node.value < value:
+                highest_lowest = max(node.value, highest_lowest)
+                node = node.right
+
+            elif value <= node.value:
+                node = node.left
+
+            else:
+                break
+
+        print("prev:", highest_lowest)
+        print()
+        if highest_lowest == 0:
+            return None
+        return highest_lowest
+
+    def next(self, value):
+        node = self.root
+
+        if node is None:
+            return None
+
+        lowest_highest = math.inf
+        while node:
+            print(value, node, lowest_highest)
+            if value < node.value:
+                lowest_highest = min(node.value, lowest_highest)
+                node = node.left
+
+            elif node.value <= value:
+                node = node.right
+
+            else:
+                break
+
+        print("next:", lowest_highest)
+        print()
+        if lowest_highest == math.inf:
+            return None
+        return lowest_highest
+
+
+if __name__ == "__main__":
+    numbers = TreeSet()
+
+    numbers.add(3)
+    numbers.add(2)
+    numbers.add(5)
+    numbers.add(7)
+
+    assert numbers.prev(5) == 3
+    assert numbers.prev(4) == 3
+    assert numbers.prev(3) == 2
+    assert numbers.prev(2) == None
+
+    assert numbers.next(4) == 5
+    assert numbers.next(5) == 7
+    assert numbers.next(6) == 7
+    assert numbers.next(7) == None
+
+    numbers = TreeSet()
+    numbers.add(1)
+    assert numbers.prev(2) == 1
+    assert numbers.next(2) == None
+    numbers.add(2)
+    assert numbers.prev(2) == 1
+    assert numbers.next(2) == None
+    numbers.add(2)
+    assert numbers.prev(3) == 2
+    assert numbers.next(1) == 2
diff --git a/viikko12/treeheight.py b/viikko12/treeheight.py
new file mode 100644
index 0000000..da62eba
--- /dev/null
+++ b/viikko12/treeheight.py
@@ -0,0 +1,64 @@
+import random
+import time
+
+
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.left = None
+        self.right = None
+
+
+class TreeSet:
+    def __init__(self):
+        self.root = None
+        self.max_depth = -1
+
+    def add(self, value):
+        max_depth = 0
+
+        if not self.root:
+            self.root = Node(value)
+            self.max_depth += 1
+            return
+
+        node = self.root
+        while True:
+            if node.value == value:
+                break
+            max_depth += 1
+            if node.value > value:
+                if not node.left:
+                    node.left = Node(value)
+                    break
+                node = node.left
+            else:
+                if not node.right:
+                    node.right = Node(value)
+                    break
+                node = node.right
+
+        self.max_depth = max(self.max_depth, max_depth)
+
+    def height(self):
+        return self.max_depth
+
+
+if __name__ == "__main__":
+    start = time.time()
+    numbers_smallest = TreeSet()
+    for i in range(1000):
+        numbers_smallest.add(i)
+    result_smallest = numbers_smallest.height()
+    end_smallest = time.time()
+
+    numbers_biggest = TreeSet()
+    for i in sorted([i for i in range(1000)], key=lambda x: random.random()):
+        numbers_biggest.add(i)
+    result_biggest = numbers_biggest.height()
+    end_biggest = time.time()
+
+    print(
+        f"Total: {end_biggest - start:.2f}, smallest: {end_smallest - start:.2f}, biggest: {end_biggest - end_smallest:.2f}"
+    )
+    print("Height smallest:", result_smallest, "Height biggest", result_biggest)
diff --git a/viikko12/treeremove.py b/viikko12/treeremove.py
new file mode 100644
index 0000000..a60c466
--- /dev/null
+++ b/viikko12/treeremove.py
@@ -0,0 +1,67 @@
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.left = None
+        self.right = None
+
+
+class TreeSet:
+    def __init__(self):
+        self.root = None
+
+    def add(self, value):
+        if not self.root:
+            self.root = Node(value)
+            return
+
+        node = self.root
+        while True:
+            if node.value == value:
+                return
+            if node.value > value:
+                if not node.left:
+                    node.left = Node(value)
+                    return
+                node = node.left
+            else:
+                if not node.right:
+                    node.right = Node(value)
+                    return
+                node = node.right
+
+    def remove(self, value):
+        pass
+
+    def __repr__(self):
+        items = []
+        self.traverse(self.root, items)
+        return str(items)
+
+    def traverse(self, node, items):
+        if not node:
+            return
+        self.traverse(node.left, items)
+        items.append(node.value)
+        self.traverse(node.right, items)
+
+
+if __name__ == "__main__":
+    numbers = TreeSet()
+
+    numbers.add(3)
+    numbers.add(2)
+    numbers.add(5)
+    numbers.add(7)
+    print(numbers)  # [2, 3, 5, 7]
+
+    numbers.remove(3)
+    print(numbers)  # [2, 5, 7]
+
+    numbers.remove(7)
+    print(numbers)  # [2, 5]
+
+    numbers.remove(2)
+    print(numbers)  # [5]
+
+    numbers.remove(5)
+    print(numbers)  # []
diff --git a/viikko12/treesize.py b/viikko12/treesize.py
new file mode 100644
index 0000000..a2366d8
--- /dev/null
+++ b/viikko12/treesize.py
@@ -0,0 +1,50 @@
+class Node:
+    def __init__(self, value):
+        self.value = value
+        self.left = None
+        self.right = None
+
+
+class TreeSet:
+    def __init__(self):
+        self.root = None
+        self.size = 0
+
+    def add(self, value):
+        if not self.root:
+            self.root = Node(value)
+            self.size += 1
+            return
+
+        node = self.root
+        while True:
+            if node.value == value:
+                return
+            if node.value > value:
+                if not node.left:
+                    self.size += 1
+                    node.left = Node(value)
+                    return
+                node = node.left
+            else:
+                if not node.right:
+                    self.size += 1
+                    node.right = Node(value)
+                    return
+                node = node.right
+
+    def __len__(self):
+        return self.size
+
+
+if __name__ == "__main__":
+    numbers = TreeSet()
+    print(len(numbers))  # 0
+    numbers.add(1)
+    print(len(numbers))  # 1
+    numbers.add(2)
+    print(len(numbers))  # 2
+    numbers.add(3)
+    print(len(numbers))  # 3
+    numbers.add(2)
+    print(len(numbers))  # 3