## Algorithm

A. Extra-terrestrial Intelligence
time limit per test
2 seconds
memory limit per test
64 megabytes
input
input.txt
output
output.txt

Recently Vasya got interested in finding extra-terrestrial intelligence. He made a simple extra-terrestrial signals’ receiver and was keeping a record of the signals for n days in a row. Each of those n days Vasya wrote a 1 in his notebook if he had received a signal that day and a 0 if he hadn’t. Vasya thinks that he has found extra-terrestrial intelligence if there is a system in the way the signals has been received, i.e. if all the intervals between successive signals are equal. Otherwise, Vasya thinks that the signals were sent by some stupid aliens no one cares about. Help Vasya to deduce from the information given by the receiver if he has found extra-terrestrial intelligence or not.

Input

The first line contains integer n (3 ≤ n ≤ 100) — amount of days during which Vasya checked if there were any signals. The second line contains n characters 1 or 0 — the record Vasya kept each of those n days. It’s guaranteed that the given record sequence contains at least three 1s.

Output

If Vasya has found extra-terrestrial intelligence, output YES, otherwise output NO.

Examples
input
Copy
`800111000`
output
Copy
`YES`
input
Copy
`71001011`
output
Copy
`NO`
input
Copy
`71010100`
output
Copy
`YES`

## Code Examples

### #1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <cstdio>

int main(){

FILE * inputFile = fopen("input.txt","r");
int n(0); fscanf(inputFile, "%d\n", &n);

int lastSignal(-1), distance(-1);
bool output(1);

for(int p = 0; p < n; p++){
char temp('0'); fscanf(inputFile, "%c", &temp);
if(temp == '1'){
if(lastSignal < 0){lastSignal = p;}
else if(distance < 0){distance = p - lastSignal; lastSignal = p;}
else if(p - lastSignal == distance){lastSignal = p;}
else if(p - lastSignal != distance){output = 0; break;}

printf("%d %d %d\n", p, lastSignal, distance);

}
}
fclose(inputFile);

FILE * outputFile = fopen("output.txt","w");
if(output){fprintf(outputFile, "YES\n");}
else{fprintf(outputFile, "NO\n");}
fclose(outputFile);

return 0;
}``````
Copy The Code &

Input

cmd
8
00111000

Output

cmd
YES