CF Round 427 D. Palindromic characteristics

题目链接：http://codeforces.com/contest/835/problem/

思路：dp[i][j]表示子串[i, j]的阶数，则：

dp[i][i] = 1;

dp[i][i + 1] = (str[i] == str[i + 1])? 2: 0;

if(str[i] != str[j] || dp[i + 1][j - 1] == 0)

　　dp[i][j] = 0;
else　　

　　dp[i][j] = dp[i][i + (j - i + 1) / 2 - 1] + 1;

而所有的k阶回文串必定是k - 1, k - 2....1阶回文川，因此 cnt[i] += sum(cnt[i + 1 -> len])

代码：

 1 const int inf = 0x3f3f3f3f;
 2 const int maxn = 5e3 + 5; 
 3 
 4 int dp[maxn][maxn], cnt[maxn];
 5 char str[maxn];
 6 
 7 int main(){
 8     memset(dp, 0, sizeof(dp));
 9     memset(cnt, 0, sizeof(cnt));
10     scanf("%s", &str[1]);
11     int slen = strlen(str + 1);
12     for(int i = 1; i <= slen; i++) dp[i][i] = 1;
13     for(int i = slen - 1; i > 0; i--){
14         dp[i][i + 1] = str[i] == str[i + 1]? 2: 0;
15         for(int j = i + 2; j <= slen; j++){
16             if(str[i] != str[j] || dp[i + 1][j - 1] == 0) dp[i][j] = 0;
17             else dp[i][j] = dp[i][i + (j - i + 1) / 2 - 1] + 1;
18         }
19     }
20     for(int i = 1; i <= slen; i++){
21         for(int j = i; j <= slen; j++){
22 //            debug
23 //            printf("[%d, %d]: %d
", i, j, dp[i][j]);
24             cnt[dp[i][j]]++;
25         }
26     }
27     for(int i = 1; i <= slen; i++){
28         for(int j = i + 1; j <= slen; j++){
29             cnt[i] += cnt[j];
30         }
31     }
32     for(int i = 1; i <= slen; i++){
33         printf("%d", cnt[i]);
34         if(i != slen) putchar(' ');
35         else puts("");
36     }
37 }

题目：

Palindromic characteristics of string s with length |s| is a sequence of |s| integers, where k-th number is the total number of non-empty substrings of s which are k-palindromes.

A string is 1-palindrome if and only if it reads the same backward as forward.

A string is k-palindrome (k > 1) if and only if:

Its left half equals to its right half.
Its left and right halfs are non-empty (k - 1)-palindromes.

The left half of string t is its prefix of length ⌊|t| / 2⌋, and right half — the suffix of the same length. ⌊|t| / 2⌋ denotes the length of string tdivided by 2, rounded down.

Note that each substring is counted as many times as it appears in the string. For example, in the string "aaa" the substring "a" appears 3 times.

Input

The first line contains the string s (1 ≤ |s| ≤ 5000) consisting of lowercase English letters.

Output

Print |s| integers — palindromic characteristics of string s.

Examples

input

abba

output

6 1 0 0

input

abacaba

output

12 4 1 0 0 0 0

Note

In the first example 1-palindromes are substring «a», «b», «b», «a», «bb», «abba», the substring «bb» is 2-palindrome. There are no 3- and 4-palindromes here.