Cantor expansion & inverse expansion c++ implementation

Cantor expands:

#include <iostream>

using namespace std;

int board[10]{1,1,2,6,24,120,720,5040,40320,362880};//Factorial of 0-9
bool book[10]; //Whether the number of marks has already appeared

int main(){
	
	string s;
	cin>>s;
	int sum = 1;
	for(int i=0 ; i<s.length() ; i++){
		int mid = s[i]-'0';
		int t = 0;
		for(int j=1 ; j<mid ; j++){
			if(book[j] == false)t++;
		}
		sum += t*board[s.length()-i-1];
		book[mid] = true;
	}
	cout<<sum<<endl;
	
	return 0;
}

Cantor's inverse expansion:

#include<iostream>

using namespace std;

int board[10]{1,1,2,6,24,120,720,5040,40320,362880};//Factorial of 0-9

bool book[10];//Whether the number of tags has appeared

int main(){
	
	string s;
	cin>>s;
	int N;
	cin>>N;
	N--;
	for(int i=s.length() ; i>=1 ; i--){
		int mid = N/board[i-1]+1;
		for(int i=1 ; i<=mid ; i++){
			if(book[i])mid++;
		}
		book[mid] = true;
		cout<<mid;
		N %= board[i-1];
	}
	
	return 0;
}