English · Original
Chinese · Translation
Formal · Original
_Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?_
Given an integer sequence _a_1, _a_2, ..., _a__n_ of length _n_. Decide whether it is possible to divide it into an odd number of non-empty subsegments, the each of which has an odd length and begins and ends with odd numbers.
A subsegment is a contiguous slice of the whole sequence. For example, {3, 4, 5} and {1} are subsegments of sequence {1, 2, 3, 4, 5, 6}, while {1, 2, 4} and {7} are not.
## Input
The first line of input contains a non-negative integer _n_ (1 ≤ _n_ ≤ 100) — the length of the sequence.
The second line contains _n_ space-separated non-negative integers _a_1, _a_2, ..., _a__n_ (0 ≤ _a__i_ ≤ 100) — the elements of the sequence.
## Output
Output "_Yes_" if it's possible to fulfill the requirements, and "_No_" otherwise.
You can output each letter in any case (upper or lower).
[samples]
## Note
In the first example, divide the sequence into 1 subsegment: {1, 3, 5} and the requirements will be met.
In the second example, divide the sequence into 3 subsegments: {1, 0, 1}, {5}, {1}.
In the third example, one of the subsegments must start with 4 which is an even number, thus the requirements cannot be met.
In the fourth example, the sequence can be divided into 2 subsegments: {3, 9, 9}, {3}, but this is not a valid solution because 2 is an even number.
_Where do odds begin, and where do they end? Where does hope emerge, and will they ever break?_
给定一个长度为 #cf_span[n] 的整数序列 #cf_span[a1, a2, ..., an]。判断是否能将其划分为奇数个非空子段，使得每个子段的长度为奇数，且首尾元素均为奇数。
#cf_span(class=[tex-font-style-underline], body=[subsegment]) 是整个序列的一个连续子序列。例如，#cf_span[{3, 4, 5}] 和 #cf_span[{1}] 是序列 #cf_span[{1, 2, 3, 4, 5, 6}] 的子段，而 #cf_span[{1, 2, 4}] 和 #cf_span[{7}] 则不是。
输入的第一行包含一个非负整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 100]) —— 序列的长度。
第二行包含 #cf_span[n] 个用空格分隔的非负整数 #cf_span[a1, a2, ..., an] (#cf_span[0 ≤ ai ≤ 100]) —— 序列的元素。
如果能满足要求，输出 "_Yes_"；否则输出 "_No_"。
你可以以任意大小写输出每个字母。
在第一个例子中，将序列划分为 #cf_span[1] 个子段：#cf_span[{1, 3, 5}]，即可满足要求。
在第二个例子中，将序列划分为 #cf_span[3] 个子段：#cf_span[{1, 0, 1}]、#cf_span[{5}]、#cf_span[{1}]。
在第三个例子中，某个子段必须以 #cf_span[4] 开头，而 4 是偶数，因此无法满足要求。
在第四个例子中，序列可以划分为 #cf_span[2] 个子段：#cf_span[{3, 9, 9}]、#cf_span[{3}]，但这不是合法解，因为 #cf_span[2] 是偶数。
## Input
输入的第一行包含一个非负整数 #cf_span[n] (#cf_span[1 ≤ n ≤ 100]) —— 序列的长度。第二行包含 #cf_span[n] 个用空格分隔的非负整数 #cf_span[a1, a2, ..., an] (#cf_span[0 ≤ ai ≤ 100]) —— 序列的元素。
## Output
如果能满足要求，输出 "_Yes_"；否则输出 "_No_"。你可以以任意大小写输出每个字母。
[samples]
## Note
在第一个例子中，将序列划分为 #cf_span[1] 个子段：#cf_span[{1, 3, 5}]，即可满足要求。在第二个例子中，将序列划分为 #cf_span[3] 个子段：#cf_span[{1, 0, 1}]、#cf_span[{5}]、#cf_span[{1}]。在第三个例子中，某个子段必须以 #cf_span[4] 开头，而 4 是偶数，因此无法满足要求。在第四个例子中，序列可以划分为 #cf_span[2] 个子段：#cf_span[{3, 9, 9}]、#cf_span[{3}]，但这不是合法解，因为 #cf_span[2] 是偶数。
**Definitions**
Let $ n \in \mathbb{Z}_{\geq 0} $ be the length of the sequence.
Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of non-negative integers.
A *subsegment* is a contiguous subsequence $ (a_i, a_{i+1}, \dots, a_j) $ for some $ 1 \leq i \leq j \leq n $.
A subsegment is *valid* if:
- Its length $ j - i + 1 $ is odd,
- Both endpoints $ a_i $ and $ a_j $ are odd.
**Constraints**
1. $ 1 \leq n \leq 100 $
2. $ 0 \leq a_i \leq 100 $ for all $ i \in \{1, \dots, n\} $
**Objective**
Determine whether there exists a partition of $ A $ into $ k $ non-overlapping, contiguous, valid subsegments, such that:
- $ k $ is an odd positive integer,
- Every element of $ A $ belongs to exactly one subsegment.
Output "Yes" if such a partition exists; otherwise, output "No".
API Response (JSON)
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