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≤200000, 1≤q≤200000)− 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
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".