DOSA  Lalith Dosa
Lalith is going to have dinner and he has N dosas in front of him with their prices represented by sequence of integers a1, a2, a3 ... an.
And he has decided to eat in a different manner. You are free to replace the price of any dosa with any positive integer.
How many prices (integers) must be replaced to make the resulting sequence strictly increasing?
Input
The first line of the test case contains an integer N  the number of dosas.
The next line contains N space separated integers where the ith integer is ai, representing the price of the ith dosa.
Output
Output the minimal number of prices(integers) that should be replaced to make the sequence strictly increasing.
Constraints
0 < N <= 10^6
0 < ai <= 10^9
Sample Input #1
6
1 7 10 2 20 22
Sample Output #1
1
Sample Input #2
5
1 2 2 3 4
Sample Output #2
3
Explanation
In the first sample input, we can replace 2 with any integer between 11 and 19 to make the price sequence strictly increasing, hence the output is 1.
In the second sample input, we can obtain 1, 2, 3, 4, 5 by changing the last three elements of the price sequence.
hide comments
vank:
20140208 01:38:34
getting WA...


Mitch Schwartz:
20140206 14:37:52
@Ashwini: "You are free to replace the price of any dosa with any positive integer." So changing to zero is not allowed. (I know that in e.g. French the word that closely resembles "positive" includes zero, but that is not the case in English.) Last edit: 20140110 15:20:16 

Ashwini:
20140206 14:38:14
by changing are we suppose to confine our operations to only increasing that particular number???


anurag garg:
20140208 01:38:22
@author

Added by:  Arun Lakshman 
Date:  20140109 
Time limit:  0.5s1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: ASM64 
Resource:  Own 