Codeforces 750E New Year and Old Subsequence 线段树优化区间DP

E. New Year and Old Subsequence

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

A string t is called nice if a string "2017" occurs in t as a subsequence but a string "2016" doesn't occur in t as a subsequence. For example, strings "203434107" and "9220617" are nice, while strings "20016", "1234" and "20167" aren't nice.

The ugliness of a string is the minimum possible number of characters to remove, in order to obtain a nice string. If it's impossible to make a string nice by removing characters, its ugliness is  - 1.

Limak has a string s of length n, with characters indexed 1 through n. He asks you q queries. In the i-th query you should compute and print the ugliness of a substring (continuous subsequence) of s starting at the index ai and ending at the index bi (inclusive).

Input

The first line of the input contains two integers n and q (4 ≤ n ≤ 200 000, 1 ≤ q ≤ 200 000) — the length of the string s and the number of queries respectively.

The second line contains a string s of length n. Every character is one of digits '0'–'9'.

The i-th of next q lines contains two integers ai and bi (1 ≤ ai ≤ bi ≤ n), describing a substring in the i-th query.

Output

For each query print the ugliness of the given substring.

Examples

input

output

input

output

input

output

Note

In the first sample:

  • In the first query, ugliness("20166766") = 4 because all four sixes must be removed.
  • In the second query, ugliness("2016676") = 3 because all three sixes must be removed.
  • In the third query, ugliness("0166766") =  - 1 because it's impossible to remove some digits to get a nice string.

In the second sample:

  • In the second query, ugliness("01201666209167") = 2. It's optimal to remove the first digit '2' and the last digit '6', what gives a string "010166620917", which is nice.
  • In the third query, ugliness("016662091670") = 1. It's optimal to remove the last digit '6', what gives a nice string "01666209170".

题意

给定一个长度小于10w的数字序列,每次询问一个区间,删除最少的字符后,能包含2017子序列但是不包含2016子序列。

思路

用线段树维护一个dp[i][j]表示从区间的起点,起始位状态i,到区间的终点,状态为j的时候的所需要删除的字符的最少的个数。其中0表示前面没有包含任何关于“2017”的子序列,1表示包含子序列1,2表示包含子序列12,依次类推,特别注意在3、4状态的时候的花费。不可能的状态标记为-1即可。查询的合并下区下区间的DP值即可。