F - Number of Digits /

### 制約

• 1 \leq S \leq 10^8

### 入力

S


### 入力例 1

1


### 出力例 1

9


### 入力例 2

2


### 出力例 2

98


### 入力例 3

123


### 出力例 3

460191684


### 入力例 4

36018


### 出力例 4

966522825


### 入力例 5

1000


### 出力例 5

184984484


Score : 900 points

### Problem Statement

For a positive integer n, let us define f(n) as the number of digits in base 10.

You are given an integer S. Count the number of the pairs of positive integers (l, r) (l \leq r) such that f(l) + f(l + 1) + ... + f(r) = S, and find the count modulo 10^9 + 7.

### Constraints

• 1 \leq S \leq 10^8

### Input

Input is given from Standard Input in the following format:

S


### Sample Input 1

1


### Sample Output 1

9


There are nine pairs (l, r) that satisfies the condition: (1, 1), (2, 2), ..., (9, 9).

### Sample Input 2

2


### Sample Output 2

98


There are 98 pairs (l, r) that satisfies the condition, such as (1, 2) and (33, 33).

### Sample Input 3

123


### Sample Output 3

460191684


### Sample Input 4

36018


### Sample Output 4

966522825


### Sample Input 5

1000


### Sample Output 5

184984484