Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 15}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = -30.
Define task_1_bound_static = 13.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    n = len(list_2)
    leftSum = [0] * n
    for i in range(1, n):
        leftSum[i] = leftSum[i - 1] + list_2[i - 1]
    total = sum(list_2)
    answer = []
    for i in range(n):
        rightSum_i = total - list_2[i] - leftSum[i]
        answer.append(abs(leftSum[i] - rightSum_i))
    python_result_2 = answer
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    s = set()
    for n in list_3:
        i = 2
        while i <= n // i:
            if n % i == 0:
                s.add(i)
                while n % i == 0:
                    n //= i
            i += 1
        if n > 1:
            s.add(n)
    python_result_3 = len(s)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -61}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [50, -95, 77, 38, -5, 96, -96, 29, 48, 93].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    n = len(list_2)
    ans = [0] * n
    for i in range(n - 1, -1, -1):
        while stk and list_2[stk[-1]] <= list_2[i]:
            stk.pop()
        if stk:
            ans[i] = stk[-1] - i
        stk.append(i)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -48}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 55.
Define task_1_bound_static = 89.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    for x in list_2:
        if x > 0:
            stk.append(x)
        else:
            while stk and stk[-1] > 0 and (stk[-1] < -x):
                stk.pop()
            if stk and stk[-1] == -x:
                stk.pop()
            elif not stk or stk[-1] < 0:
                stk.append(x)
    python_result_2 = stk
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [58, 8, -47, -10, 61, -77, -14, 80, -41, 64]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    f = True
    while f:
        f = False
        t = list_1[:]
        for i in range(1, len(t) - 1):
            if t[i] > t[i - 1] and t[i] > t[i + 1]:
                list_1[i] -= 1
                f = True
            if t[i] < t[i - 1] and t[i] < t[i + 1]:
                list_1[i] += 1
                f = True
    python_result_1 = list_1
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    def reverse(arr, j):
        i = 0
        while i < j:
            (arr[i], arr[j]) = (arr[j], arr[i])
            (i, j) = (i + 1, j - 1)
    n = len(list_2)
    ans = []
    for i in range(n - 1, 0, -1):
        j = i
        while j > 0 and list_2[j] != i + 1:
            j -= 1
        if j < i:
            if j > 0:
                ans.append(j + 1)
                reverse(list_2, j)
            ans.append(i + 1)
            reverse(list_2, i)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 92}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [17, -22, 90, -82, 23, -20, 66, 18, -42, 89].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_limit_static = 20.
Trace the execution of task_2 with inputs limit = task_2_limit_static.
```python
from typing import List
def task_2(list_2: List[int], limit: int) -> List[int]:
    n = len(list_2)
    arr = sorted(zip(list_2, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= limit:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-55, -96, 91, 76, -22, -27, 79, -69, 56, 86]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    (i, n) = (0, len(list_1))
    while i + 1 < n and list_1[i] < list_1[i + 1]:
        i += 1
    if i == n - 1:
        python_result_1 = n * (n + 1) // 2
        return python_result_1
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_1[i] >= list_1[j]:
            i -= 1
        ans += i + 2
        if list_1[j - 1] >= list_1[j]:
            break
        j -= 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [26, -43, -19, 59, 25, 36, -41, -62, -97, 92].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [33, -44, -45, 22, 3, -55, 37, 17, -33, -17]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_k_static = -34.
Trace the execution of task_1 with inputs k = task_1_k_static.
```python
from typing import List
def task_1(list_1: List[int], k: int) -> int:
    mx = max(list_1)
    n = len(list_1)
    ans = cnt = j = 0
    for x in list_1:
        while j < n and cnt < k:
            cnt += list_1[j] == mx
            j += 1
        if cnt < k:
            break
        ans += n - j + 1
        cnt -= x == mx
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = 4.
Define task_2_bound_static = 8.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -34}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-85, 95, 30, 3, -78, -61, 67, 11, 75, 51].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    n = len(list_2)
    ans = [0] * n
    for i in range(n - 1, -1, -1):
        while stk and list_2[stk[-1]] <= list_2[i]:
            stk.pop()
        if stk:
            ans[i] = stk[-1] - i
        stk.append(i)
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -12}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    ans = 0
    (mi, mx) = (-2 ** 31, 2 ** 31 - 1)
    while val_1:
        if ans < mi // 10 + 1 or ans > mx // 10:
            python_result_1 = 0
            return python_result_1
        y = val_1 % 10
        if val_1 < 0 and y > 0:
            y -= 10
        ans = ans * 10 + y
        val_1 = (val_1 - y) // 10
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-41, 93, 21, 79, 16, -32, -41, 32, 33, 56].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -31}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = -79.
Define task_1_bound_static = 62.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    stk = []
    for x in list_2:
        if x > 0:
            stk.append(x)
        else:
            while stk and stk[-1] > 0 and (stk[-1] < -x):
                stk.pop()
            if stk and stk[-1] == -x:
                stk.pop()
            elif not stk or stk[-1] < 0:
                stk.append(x)
    python_result_2 = stk
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 36}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_tokens_static = [9, -17, 47, -98, 75, -90, -22, -100, 52, 87].
Trace the execution of task_1 with inputs tokens = task_1_tokens_static.
```python
from typing import List
def task_1(tokens: List[int], val_1: int) -> int:
    tokens.sort()
    ans = score = 0
    (i, j) = (0, len(tokens) - 1)
    while i <= j:
        if val_1 >= tokens[i]:
            val_1 -= tokens[i]
            (score, i) = (score + 1, i + 1)
            ans = max(ans, score)
        elif score:
            val_1 += tokens[j]
            (score, j) = (score - 1, j - 1)
        else:
            break
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = -73.
Define task_2_bound_static = 15.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-82, -86, -34, -17, -57, -51, -72, -91, 28, -52]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    n = len(list_1)
    ans = [0] * n
    stk = []
    for i in range(n - 1, -1, -1):
        while stk and stk[-1] < list_1[i]:
            ans[i] += 1
            stk.pop()
        if stk:
            ans[i] += 1
        stk.append(list_1[i])
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_limit_static = -71.
Trace the execution of task_2 with inputs limit = task_2_limit_static.
```python
from typing import List
def task_2(list_2: List[int], limit: int) -> List[int]:
    n = len(list_2)
    arr = sorted(zip(list_2, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= limit:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -11}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-40, 33, -74, 67, 75, 78, 60, -95, 40, -52].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> int:
    nums.sort()
    n = len(nums)
    m = n >> 1
    ans = abs(nums[m] - val_1)
    if nums[m] > val_1:
        for i in range(m - 1, -1, -1):
            if nums[i] <= val_1:
                break
            ans += nums[i] - val_1
    else:
        for i in range(m + 1, n):
            if nums[i] >= val_1:
                break
            ans += val_1 - nums[i]
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [-79, 98, 95, 12, -1, -10, 78, -76, 52, -1].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [16, 83, -94, -35, 68, -16, 26, 40, -44, -75]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    n = len(list_1)
    left = [1] * n
    right = [1] * n
    for i in range(1, n):
        if list_1[i] > list_1[i - 1]:
            left[i] = left[i - 1] + 1
    for i in range(n - 2, -1, -1):
        if list_1[i] > list_1[i + 1]:
            right[i] = right[i + 1] + 1
    python_result_1 = sum((max(a, b) for (a, b) in zip(left, right)))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_y_static = -62.
Define task_2_bound_static = 43.
Trace the execution of task_2 with inputs y = task_2_y_static, bound = task_2_bound_static.
```python
from typing import List
def task_2(val_2: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_2 == 1:
            break
        a *= val_2
    python_result_2 = list(ans)
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 62}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    s = list(str(val_1))
    i = 1
    while i < len(s) and s[i - 1] <= s[i]:
        i += 1
    if i < len(s):
        while i and s[i - 1] > s[i]:
            s[i - 1] = str(int(s[i - 1]) - 1)
            i -= 1
        i += 1
        while i < len(s):
            s[i] = '9'
            i += 1
    python_result_1 = int(''.join(s))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_nums_static = [83, -29, 86, -39, 1, -92, -86, -23, 1, 9].
Trace the execution of task_2 with inputs nums = task_2_nums_static.
```python
from typing import List
def task_2(nums: List[int], val_2: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_2:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [54, 93, 0, 97, -7, 99, -24, -55, 19, 85]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_limit_static = 96.
Trace the execution of task_1 with inputs limit = task_1_limit_static.
```python
from typing import List
def task_1(list_1: List[int], limit: int) -> List[int]:
    n = len(list_1)
    arr = sorted(zip(list_1, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= limit:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    n = len(list_2)
    suf = [0] * (n + 1)
    s = set()
    for i in range(n - 1, -1, -1):
        s.add(list_2[i])
        suf[i] = len(s)
    s.clear()
    ans = [0] * n
    for (i, x) in enumerate(list_2):
        s.add(x)
        ans[i] = len(s) - suf[i + 1]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-10, 25, -93, 13, 6, -41, -31, -75, 72, -45]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    list_1.sort()
    n = len(list_1)
    f = [1] * n
    k = 0
    for i in range(n):
        for j in range(i):
            if list_1[i] % list_1[j] == 0:
                f[i] = max(f[i], f[j] + 1)
        if f[k] < f[i]:
            k = i
    m = f[k]
    i = k
    ans = []
    while m:
        if list_1[k] % list_1[i] == 0 and f[i] == m:
            ans.append(list_1[i])
            (k, m) = (i, m - 1)
        i -= 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> List[int]:
    f = True
    while f:
        f = False
        t = list_2[:]
        for i in range(1, len(t) - 1):
            if t[i] > t[i - 1] and t[i] > t[i + 1]:
                list_2[i] -= 1
                f = True
            if t[i] < t[i - 1] and t[i] < t[i + 1]:
                list_2[i] += 1
                f = True
    python_result_2 = list_2
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let list_3 be the result of preprocessing task_2_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_3 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_3.
```python
from typing import List
def task_3(list_3: List[int]) -> int:
    n = len(list_3)
    f = [0] * n
    g = [0] * n
    f[0] = int(list_3[0] > 0)
    g[0] = int(list_3[0] < 0)
    ans = f[0]
    for i in range(1, n):
        if list_3[i] > 0:
            f[i] = f[i - 1] + 1
            g[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
        elif list_3[i] < 0:
            f[i] = 0 if g[i - 1] == 0 else g[i - 1] + 1
            g[i] = f[i - 1] + 1
        ans = max(ans, f[i])
    python_result_3 = ans
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 28}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [37, 68, 42, -15, -72, -31, 24, -16, 81, -96].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    ans = 1
    f = [1] * n
    g = [1] * n
    for i in range(1, n):
        for j in range(i):
            if list_2[j] < list_2[i]:
                f[i] = max(f[i], g[j] + 1)
            elif list_2[j] > list_2[i]:
                g[i] = max(g[i], f[j] + 1)
        ans = max(ans, f[i], g[i])
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -11.
Define task_3_bound_static = 74.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [86, 43, 22, -75, -58, 24, -65, -83, -3, -33]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    f = True
    while f:
        f = False
        t = list_1[:]
        for i in range(1, len(t) - 1):
            if t[i] > t[i - 1] and t[i] > t[i + 1]:
                list_1[i] -= 1
                f = True
            if t[i] < t[i - 1] and t[i] < t[i + 1]:
                list_1[i] += 1
                f = True
    python_result_1 = list_1
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_queries_static = [-12, -6, 76, 97, -2, 67, 94, -100, -37, -52].
Trace the execution of task_2 with inputs queries = task_2_queries_static.
```python
from typing import List
def task_2(list_2: List[int], queries: List[int]) -> int:
    n = len(list_2)
    f = [[0] * n for _ in range(n)]
    m = len(queries)
    for i in range(n):
        for j in range(n - 1, i - 1, -1):
            if i:
                f[i][j] = max(f[i][j], f[i - 1][j] + (list_2[i - 1] >= queries[f[i - 1][j]]))
            if j + 1 < n:
                f[i][j] = max(f[i][j], f[i][j + 1] + (list_2[j + 1] >= queries[f[i][j + 1]]))
            if f[i][j] == m:
                python_result_2 = m
                return python_result_2
    python_result_2 = max((f[i][i] + (list_2[i] >= queries[f[i][i]]) for i in range(n)))
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -56.
Define task_3_bound_static = 42.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [26, -43, 46, 58, -17, 16, 42, 54, -99, -94]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Define task_1_target_static = 23.
Trace the execution of task_1 with inputs target = task_1_target_static.
```python
from typing import List
def task_1(list_1: List[int], target: int) -> int:
    list_1.sort()
    (ans, n) = (0, len(list_1))
    for i in range(n - 2):
        (j, k) = (i + 1, n - 1)
        while j < k:
            x = list_1[i] + list_1[j] + list_1[k]
            if x < target:
                ans += k - j
                j += 1
            else:
                k -= 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_arr_static = [59, -7, -81, 33, 86, -36, -56, -75, 60, 41].
Trace the execution of task_2 with inputs arr = task_2_arr_static.
```python
from typing import List
def task_2(arr: List[int], val_2: int) -> int:
    mx = arr[0]
    cnt = 0
    for x in arr[1:]:
        if mx < x:
            mx = x
            cnt = 1
        else:
            cnt += 1
        if cnt == val_2:
            break
    python_result_2 = mx
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 3.
Define task_3_bound_static = 59.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-58, -57, -69, -29, -19, -48, -80, -3, -16, -54]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    n = len(list_1)
    leftSum = [0] * n
    for i in range(1, n):
        leftSum[i] = leftSum[i - 1] + list_1[i - 1]
    total = sum(list_1)
    answer = []
    for i in range(n):
        rightSum_i = total - list_1[i] - leftSum[i]
        answer.append(abs(leftSum[i] - rightSum_i))
    python_result_1 = answer
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Define task_2_nums2_static = [-65, -78, 15, 83, -38, -43, -14, -27, -23, -92].
Trace the execution of task_2 with inputs nums2 = task_2_nums2_static.
```python
from typing import List
def task_2(list_2: List[int], nums2: List[int]) -> int:
    def f(nums1, nums2):
        d = [a - b for (a, b) in zip(nums1, nums2)]
        t = mx = d[0]
        for v in d[1:]:
            if t > 0:
                t += v
            else:
                t = v
            mx = max(mx, t)
        return mx
    (s1, s2) = (sum(list_2), sum(nums2))
    python_result_2 = max(s2 + f(list_2, nums2), s1 + f(nums2, list_2))
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -86.
Define task_3_bound_static = 15.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -69}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    s = list(str(val_1))
    i = 1
    while i < len(s) and s[i - 1] <= s[i]:
        i += 1
    if i < len(s):
        while i and s[i - 1] > s[i]:
            s[i - 1] = str(int(s[i - 1]) - 1)
            i -= 1
        i += 1
        while i < len(s):
            s[i] = '9'
            i += 1
    python_result_1 = int(''.join(s))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_arr_static = [-51, -66, 44, -51, 62, -38, -49, -3, 35, -94].
Trace the execution of task_2 with inputs arr = task_2_arr_static.
```python
from typing import List
def task_2(arr: List[int], val_2: int) -> int:
    mx = arr[0]
    cnt = 0
    for x in arr[1:]:
        if mx < x:
            mx = x
            cnt = 1
        else:
            cnt += 1
        if cnt == val_2:
            break
    python_result_2 = mx
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -59.
Define task_3_bound_static = 91.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 9}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_1.
```python
def task_1(val_1: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_1:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_1:
        ans += 1
        s += k
        k += 1
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Trace the execution of task_2.
```python
def task_2(val_2: int) -> int:
    (s, k) = (0, 1)
    while s + k * (k + 1) // 2 <= val_2:
        s += k * (k + 1) // 2
        k += 1
    k -= 1
    ans = k * (k + 1) // 2
    k = 1
    while s < val_2:
        ans += 1
        s += k
        k += 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 29.
Define task_3_bound_static = 11.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 40}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [49, -45, -4, 99, 80, -77, 64, -39, 55, 57].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    (i, n) = (0, len(list_2))
    while i + 1 < n and list_2[i] < list_2[i + 1]:
        i += 1
    if i == n - 1:
        python_result_2 = n * (n + 1) // 2
        return python_result_2
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_2[i] >= list_2[j]:
            i -= 1
        ans += i + 2
        if list_2[j - 1] >= list_2[j]:
            break
        j -= 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 61.
Define task_3_bound_static = 38.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [73, 25, 21, -2, 59, 64, 68, -12, 61, -12]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    n = len(list_1)
    ans = [-1] * n
    stk = []
    for i in range(n * 2 - 1, -1, -1):
        i %= n
        while stk and stk[-1] <= list_1[i]:
            stk.pop()
        if stk:
            ans[i] = stk[-1]
        stk.append(list_1[i])
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    n = len(list_2)
    ans = 1
    f = [1] * n
    g = [1] * n
    for i in range(1, n):
        for j in range(i):
            if list_2[j] < list_2[i]:
                f[i] = max(f[i], g[j] + 1)
            elif list_2[j] > list_2[i]:
                g[i] = max(g[i], f[j] + 1)
        ans = max(ans, f[i], g[i])
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -47.
Define task_3_bound_static = 72.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": 2}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_y_static = 20.
Define task_1_bound_static = 43.
Trace the execution of task_1 with inputs y = task_1_y_static, bound = task_1_bound_static.
```python
from typing import List
def task_1(val_1: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_1 == 1:
            break
        a *= val_1
    python_result_1 = list(ans)
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    (i, n) = (0, len(list_2))
    while i + 1 < n and list_2[i] < list_2[i + 1]:
        i += 1
    if i == n - 1:
        python_result_2 = n * (n + 1) // 2
        return python_result_2
    ans = i + 2
    j = n - 1
    while j:
        while i >= 0 and list_2[i] >= list_2[j]:
            i -= 1
        ans += i + 2
        if list_2[j - 1] >= list_2[j]:
            break
        j -= 1
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 31.
Define task_3_bound_static = 95.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -95}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_nums_static = [-46, -9, 36, 12, -41, 93, -64, 17, -37, -92].
Trace the execution of task_1 with inputs nums = task_1_nums_static.
```python
from typing import List
def task_1(nums: List[int], val_1: int) -> List[int]:
    n = len(nums)
    arr = sorted(zip(nums, range(n)))
    ans = [0] * n
    i = 0
    while i < n:
        j = i + 1
        while j < n and arr[j][0] - arr[j - 1][0] <= val_1:
            j += 1
        idx = sorted((k for (_, k) in arr[i:j]))
        for (k, (x, _)) in zip(idx, arr[i:j]):
            ans[k] = x
        i = j
    python_result_1 = ans
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    mod = 10 ** 9 + 7
    n = len(list_2)
    list_2.sort()
    idx = {v: i for (i, v) in enumerate(list_2)}
    f = [1] * n
    for (i, a) in enumerate(list_2):
        for j in range(i):
            b = list_2[j]
            if a % b == 0 and (c := (a // b)) in idx:
                f[i] = (f[i] + f[j] * f[idx[c]]) % mod
    python_result_2 = sum(f) % mod
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 18.
Define task_3_bound_static = 95.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [68, 83, -79, -77, -59, 19, 79, -20, -79, 96]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> List[int]:
    (i, j) = (0, len(list_1) - 1)
    while i < j:
        if list_1[i] % 2 == 0:
            i += 1
        elif list_1[j] % 2 == 1:
            j -= 1
        else:
            (list_1[i], list_1[j]) = (list_1[j], list_1[i])
            (i, j) = (i + 1, j - 1)
    python_result_1 = list_1
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let list_2 be the result of preprocessing task_1_out["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_2 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_2.
```python
from typing import List
def task_2(list_2: List[int]) -> int:
    stk = []
    ans = 0
    for x in list_2:
        while stk and stk[-1][0] < x:
            stk.pop()
        if not stk or stk[-1][0] > x:
            stk.append([x, 1])
        else:
            stk[-1][1] += 1
        ans += stk[-1][1]
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = -31.
Define task_3_bound_static = 91.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": [-75, 0, 59, 84, 33, 34, -3, -66, 6, 94]}.
Task 1:
Let list_1 be the result of preprocessing task_1_input["result"] as follows - for every element, if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
If list_1 has more than 10 elements, keep only the first 10 elements.
Trace the execution of task_1.
```python
from typing import List
def task_1(list_1: List[int]) -> int:
    n = len(list_1)
    stk = []
    left = [-1] * n
    for (i, x) in enumerate(list_1):
        while stk and list_1[stk[-1]] > x:
            stk.pop()
        if stk:
            left[i] = stk[-1]
        stk.append(i)
    stk = []
    right = [n] * n
    for i in range(n - 1, -1, -1):
        x = list_1[i]
        while stk and list_1[stk[-1]] >= x:
            stk.pop()
        if stk:
            right[i] = stk[-1]
        stk.append(i)
    f = [0] * n
    for (i, x) in enumerate(list_1):
        if i and x >= list_1[i - 1]:
            f[i] = f[i - 1] + x
        else:
            j = left[i]
            f[i] = x * (i - j) + (f[j] if j != -1 else 0)
    g = [0] * n
    for i in range(n - 1, -1, -1):
        if i < n - 1 and list_1[i] >= list_1[i + 1]:
            g[i] = g[i + 1] + list_1[i]
        else:
            j = right[i]
            g[i] = list_1[i] * (j - i) + (g[j] if j != n else 0)
    python_result_1 = max((a + b - c for (a, b, c) in zip(f, g, list_1)))
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_tokens_static = [29, 71, 88, -36, -10, -16, -59, -48, -57, -71].
Trace the execution of task_2 with inputs tokens = task_2_tokens_static.
```python
from typing import List
def task_2(tokens: List[int], val_2: int) -> int:
    tokens.sort()
    ans = score = 0
    (i, j) = (0, len(tokens) - 1)
    while i <= j:
        if val_2 >= tokens[i]:
            val_2 -= tokens[i]
            (score, i) = (score + 1, i + 1)
            ans = max(ans, score)
        elif score:
            val_2 += tokens[j]
            (score, j) = (score - 1, j - 1)
        else:
            break
    python_result_2 = ans
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 84.
Define task_3_bound_static = 72.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.


Prompt:
Solve the following tasks. Output the result for each.

Define task_1_input = {"result": -77}.
Task 1:
Let val_1 be the result of preprocessing task_1_input["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_1_arr_static = [-11, -24, -93, -38, 40, 9, -20, 85, 63, -74].
Trace the execution of task_1 with inputs arr = task_1_arr_static.
```python
from typing import List
def task_1(arr: List[int], val_1: int) -> int:
    mx = arr[0]
    cnt = 0
    for x in arr[1:]:
        if mx < x:
            mx = x
            cnt = 1
        else:
            cnt += 1
        if cnt == val_1:
            break
    python_result_1 = mx
    return python_result_1
```
Let python_result_1 be the value returned by task_1.
Output the result as task_1_out = {"result": python_result_1}, replacing python_result_1 with its calculated value.

Task 2:
Let val_2 be the result of preprocessing task_1_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_2_initialExperience_static = -5.
Define task_2_energy_static = [35, -81, -39, -45, -97, -26, 16, -10, 73, -70].
Define task_2_experience_static = [-72, 85, 71, 90, -66, -99, 51, -39, 65, 26].
Trace the execution of task_2 with inputs initialExperience = task_2_initialExperience_static, energy = task_2_energy_static, experience = task_2_experience_static.
```python
from typing import List
def task_2(val_2: int, initialExperience: int, energy: List[int], experience: List[int]) -> int:
    sum_energy = sum(energy)
    energy_hours = max(0, sum_energy + 1 - val_2)
    exp_hours = 0
    current_exp = initialExperience
    for e in experience:
        if current_exp <= e:
            delta = e + 1 - current_exp
            exp_hours += delta
            current_exp += delta
        current_exp += e
    python_result_2 = energy_hours + exp_hours
    return python_result_2
```
Let python_result_2 be the value returned by task_2.
Output the result as task_2_out = {"result": python_result_2}, replacing python_result_2 with its calculated value.

Task 3:
Let val_3 be the result of preprocessing task_2_out["result"] as follows - if it is a float, convert it to an integer by rounding ties away from zero (0.5 to 1, -0.5 to -1); then replace it with the remainder of its absolute value modulo 100 while preserving its original sign.
Define task_3_y_static = 57.
Define task_3_bound_static = 68.
Trace the execution of task_3 with inputs y = task_3_y_static, bound = task_3_bound_static.
```python
from typing import List
def task_3(val_3: int, y: int, bound: int) -> List[int]:
    ans = []
    a = 1
    while a <= bound:
        b = 1
        while a + b <= bound:
            ans.append(a + b)
            b *= y
            if y == 1:
                break
        if val_3 == 1:
            break
        a *= val_3
    python_result_3 = list(ans)
    return python_result_3
```
Let python_result_3 be the value returned by task_3.
Output the result as task_3_out = {"result": python_result_3}, replacing python_result_3 with its calculated value.