Good Bye 2016 |
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Finished |

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E. New Year and Old Subsequence

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputA 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 *a*_{i} and ending at the index *b*_{i} (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 *a*_{i} and *b*_{i} (1 ≤ *a*_{i} ≤ *b*_{i} ≤ *n*), describing a substring in the *i*-th query.

Output

For each query print the ugliness of the given substring.

Examples

Input

8 3

20166766

1 8

1 7

2 8

Output

4

3

-1

Input

15 5

012016662091670

3 4

1 14

4 15

1 13

10 15

Output

-1

2

1

-1

-1

Input

4 2

1234

2 4

1 2

Output

-1

-1

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".

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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