DZY has a sequence a, consisting of n integers.
We'll call a sequence ai, ai + 1, ..., aj(1 ≤ i ≤ j ≤ n) a subsegment of the sequence a. The value (j - i + 1) denotes the length of the subsegment.
Your task is to find the longest subsegment of a, such that it is possible to change at most one number (change one number to any integer you want) from the subsegment to make the subsegment strictly increasing.
You only need to output the length of the subsegment you find.
Input
The first line contains integer n (1 ≤ n ≤ 105). The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109).
Output
In a single line print the answer to the problem — the maximum length of the required subsegment.
Examples
Input
Copy
6
7 2 3 1 5 6
Output
Copy
5
Note
You can choose subsegment a2, a3, a4, a5, a6 and change its 3rd element (that is a4) to 4.
问最多修改一个数字,序列可获得地最大严格递增字段长度为多大;
考虑dp;
dp1 表示以 i 位置结尾的最长子段长度;
dp2 表示以 i 位置开头的最长子段长度;
特判一下当 n=1时,长度为1;
考虑拼接:当 x[ i+1 ]>=2+ x[ i-1 ]时,那么改变 x[ i ]即可拼接子段
#include
#include
#include
#include
#include
#include
#include
#include
EPFL - Fighting