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internbootcamp/bootcamp/cserejaandsubsequences/cserejaandsubsequences.py

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+"""# 
+
+### 谜题描述
+Sereja has a sequence that consists of n positive integers, a1, a2, ..., an. 
+
+First Sereja took a piece of squared paper and wrote all distinct non-empty non-decreasing subsequences of sequence a. Then for each sequence written on the squared paper, Sereja wrote on a piece of lines paper all sequences that do not exceed it.
+
+A sequence of positive integers x = x1, x2, ..., xr doesn't exceed a sequence of positive integers y = y1, y2, ..., yr, if the following inequation holds: x1 ≤ y1, x2 ≤ y2, ..., xr ≤ yr.
+
+Now Sereja wonders, how many sequences are written on the lines piece of paper. Help Sereja, find the required quantity modulo 1000000007 (109 + 7). 
+
+Input
+
+The first line contains integer n (1 ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 106).
+
+Output
+
+In the single line print the answer to the problem modulo 1000000007 (109 + 7).
+
+Examples
+
+Input
+
+1
+42
+
+
+Output
+
+42
+
+
+Input
+
+3
+1 2 2
+
+
+Output
+
+13
+
+
+Input
+
+5
+1 2 3 4 5
+
+
+Output
+
+719
+
+Here is a reference code to solve this task. You can use this to help you genereate cases or validate the solution.
+```python
+from sys import stdin
+def main():
+    n = int(stdin.readline())
+    a = map(int, stdin.readline().split())
+    b = [0] * (1 << 20)
+    def get(x):
+        res = 0
+        while x > 0:
+            res += b[x]
+            x &= (x - 1)
+        return res
+    def add(x, v):
+        while x < 1 << 20:
+            b[x] += v
+            x += x - (x & (x - 1))
+    mod = 1000000007
+    for x in a:
+        y = get(x) * x + x
+        s = get(x) - get(x - 1)
+        add(x, ((y - s) % mod + mod) % mod)
+    print get(10 ** 6) % mod
+main()
+```
+
+
+请完成上述谜题的训练场环境类实现，包括所有必要的方法。
+"""
+
+from bootcamp import Basebootcamp
+from bootcamp import Basebootcamp
+import random
+
+MOD = 10**9 + 7
+MAX_BIT = 20  # 使用20位二进制数表示树状数组大小
+TREE_SIZE = 1 << MAX_BIT  # 1048576，覆盖题目最大数值1e6
+
+class Cserejaandsubsequencesbootcamp(Basebootcamp):
+    def __init__(self, max_n=100, max_value=1000):
+        self.max_n = min(max_n, 10**5)     # 题目约束n≤1e5
+        self.max_value = min(max_value, 10**6)  # 题目约束ai≤1e6
+    
+    def case_generator(self):
+        """生成符合题目数值范围的测试用例"""
+        n = random.randint(1, self.max_n)
+        a = [random.randint(1, self.max_value) for _ in range(n)]
+        return {
+            'n': n,
+            'a': a,
+            'correct_answer': self.compute_answer(n, a)
+        }
+    
+    @staticmethod
+    def compute_answer(n, a):
+        """优化后的正确答案计算"""
+        tree = [0] * (TREE_SIZE + 1)  # 固定大小的树状数组
+
+        def lowbit(x): return x & -x
+        
+        def get(x):
+            res = 0
+            while x > 0:
+                res = (res + tree[x]) % MOD
+                x -= lowbit(x)
+            return res
+
+        def update(x, v):
+            while x <= TREE_SIZE:
+                tree[x] = (tree[x] + v) % MOD
+                x += lowbit(x)
+
+        for num in a:
+            prefix_sum = get(num)
+            # 计算新增值并更新树状数组
+            new_val = (prefix_sum * num + num) % MOD
+            current = (get(num) - get(num-1)) % MOD  # 获取当前值
+            delta = (new_val - current) % MOD
+            update(num, delta)
+
+        return get(TREE_SIZE) % MOD  # 查询最大值范围内的总和
+
+    @staticmethod
+    def prompt_func(question_case):
+        a_str = ' '.join(map(str, question_case['a']))
+        return f"""给定一个长度为{question_case['n']}的正整数序列：[{a_str}]
+        
+请按以下规则计算结果：
+1. 找出所有不同的非空非递减子序列y
+2. 对每个y，统计满足∀i (x_i ≤ y_i)的非空序列x的数量
+3. 将结果求和并对1e9+7取模
+
+答案格式要求：将最终答案用[answer]标签包裹，例如：[answer]123[/answer]"""
+
+    @staticmethod
+    def extract_output(output):
+        import re
+        matches = re.findall(r'\[answer\]\s*(\d+)\s*\[/answer\]', output)
+        return int(matches[-1]) % MOD if matches else None
+
+    @classmethod
+    def _verify_correction(cls, solution, identity):
+        expected = identity['correct_answer'] % MOD
+        return solution == expected if solution is not None else False