Problem:
Score : 300 points

Problem Statement

There are N people, conveniently numbered 1 through N.
They were standing in a row yesterday, but now they are unsure of the order in which they were standing.
However, each person remembered the following fact: the absolute difference of the number of the people who were standing to the left of that person, and the number of the people who were standing to the right of that person.
According to their reports, the difference above for person i is A_i.

Based on these reports, find the number of the possible orders in which they were standing.
Since it can be extremely large, print the answer modulo 10^9+7.
Note that the reports may be incorrect and thus there may be no consistent order.
In such a case, print 0.

Constraints

1≦N≦10^5

0≦A_i≦N-1

Input

The input is given from Standard Input in the following format:

N
A_1 A_2 ... A_N

Output

Print the number of the possible orders in which they were standing, modulo 10^9+7.

Sample Input 1

5
2 4 4 0 2

Sample Output 1

4

There are four possible orders, as follows:

2,1,4,5,3

2,5,4,1,3

3,1,4,5,2

3,5,4,1,2

Sample Input 2

7
6 4 0 2 4 0 2

Sample Output 2

0

Any order would be inconsistent with the reports, thus the answer is 0.

Sample Input 3

8
7 5 1 1 7 3 5 3

Sample Output 3

16

Solution in C (GCC 5.4.1) (judge verdict: Accepted)

/*
cat <<EOF >mistaken-paste
*/

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
 
#define BIG 2000000007
 
#define MOD 1000000007
typedef unsigned long long ull;
typedef   signed long long sll;

#define N_MAX 200000
#define M_MAX 200
 
typedef struct {
	int a;
	int b;
} hw;

typedef struct {
	sll a;
	sll b;
} hwll;
 

typedef struct {
	ull a;
	int i;
} struct_a;

typedef struct {
	ull cost;
	int left;
	int right;
} struct_b;


const hw vector8[8] = {
	{-1, -1},
	{-1,  0},
	{-1, +1},
	{ 0, -1},
	{ 0, +1},
	{+1, -1},
	{+1,  0},
	{+1, +1}
};
 
ull n, m;
ull h, w;
ull k;
ull va, vb, vc, vd, ve, vf;
ull a[N_MAX];
// sll a[N_MAX];
// ull wall[N_MAX][M_MAX];
ull b[N_MAX];
// sll b[N_MAX];
// char s[N_MAX + 1];
// char t[N_MAX + 1];
// char s[N_MAX][M_MAX + 1];

// ull dp[N_MAX];
// sll dp[N_MAX];
// ull dp[N_MAX + 1][N_MAX + 1];
// ull dp[N_MAX][M_MAX + 1];

// hw arr[N_MAX];
// hwll arr[N_MAX];
// hw brr[M_MAX];

// ull digitdp[102][   2][    2];
//          pos  less  carry


// struct_a arr[N_MAX * 2];
// struct_b brr[N_MAX * 2];

void swap_adj(ull *a, ull *b){
	ull tmp = *b;
	*b = *a;
	*a = tmp;
	return;
}
 
ull divide(ull a, ull b){
	ull x = MOD - 2;
	ull ans = 1;
	while (x) {
		if (x & 1) ans = (ans * b) % MOD;
		b = (b * b) % MOD;
		x /= 2;
	}
	return (a * ans) % MOD;
}
 
int digits(ull x){
	int i = 1;
	while (x >= 10) {
		x /= 10;
		i++;
	}
	return i;
}

ull umin(ull x, ull y){
	return (x < y) ? x : y;
}

ull umax(ull x, ull y){
	return (x > y) ? x : y;
}

sll smin(sll x, sll y){
	return (x < y) ? x : y;
}

sll smax(sll x, sll y){
	return (x > y) ? x : y;
}

ull gcd(ull x, ull y){
	if (x < y) {
		return gcd(y, x);
	} else if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}
 
ull bitpow(ull a, ull x){
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= MOD;
		}
		x /= 2;
		a = (a * a) % MOD;
	}
	return result;
}
 
// int nextroute(int arr[]){
// 	int i = n - 1;
// 	int j, x;
// 	while (arr[i - 1] > arr[i]) i--;
 
// 	x = n;
// 	for (j = i; j < n; j++) {
// 		if (arr[j] < arr[i - 1]) continue;
// 		if (x == n || arr[x] > arr[j]) x = j;
// 	}
// 	arr[i - 1] ^= arr[x];
// 	arr[x] ^= arr[i - 1];
// 	arr[i - 1] ^= arr[x];
 
// 	qsort(&arr[i], n - i, sizeof(int), comp);
// 	return 0;
// }
 
int targetdig(ull x, int index /* 1-indexed */){
	// static...?
	int posmax = digits(x);
	if (posmax < index) return -1;
	while (posmax > index) {
		posmax--;
		x /= 10;
	}
	return x % 10;
}

int charcmp(const char *left, const char *right){
	if (*left < *right) {
		return -1;
	} else if (*left > *right) {
		return +1;
	} else {
		return 0;
	}
}

int intcomp(const int *left, const int *right){
	if (*left < *right) {
		return -1;
	} else if (*left > *right) {
		return +1;
	} else {
		return 0;
	}
}

int ullcomp(const ull *left, const ull *right){
	if (*left < *right) {
		return -1;
	} else if (*left > *right) {
		return +1;
	} else {
		return 0;
	}
}

int sllcomp(const sll *left, const sll *right){
	if (*left < *right) {
		return -1;
	} else if (*left > *right) {
		return +1;
	} else {
		return 0;
	}
}

int hwAcomp(const hw *left, const hw *right){
	return intcomp(&(left->a), &(right->a));
}
 
int hwBcomp(const hw *left, const hw *right){
	return intcomp(&(left->b), &(right->b));
}
 
int hwABcomp(const hw *left, const hw *right){
	int x = hwAcomp(left, right);
	if (x) return x;
	return hwBcomp(left, right);
}

int hwllAcomp(const hwll *left, const hwll *right){
	return sllcomp(&(left->a), &(right->a));
}
 
int hwllBcomp(const hwll *left, const hwll *right){
	return sllcomp(&(left->b), &(right->b));
}
 
int hwllABcomp(const hwll *left, const hwll *right){
	int x = hwllAcomp(left, right);
	if (x) return x;
	return hwllBcomp(left, right);
}

// int hw_lowerbound(hw arr[], int length, const hw x){
// 	int ok = 0;
// 	int ng = length;
// 	while (ok + 1 < ng) {
// 		int med = (ok + ng) / 2;
// 		if (hwABcomp(&arr[med], &x) >= 0) {
// 			ok = med;
// 		} else {
// 			ng = med;
// 		}
// 	}
// 	return ok;
// }

// int hw_upperbound(hw arr[], int length, const hw x){
// 	int ok = 0;
// 	int ng = length;
// 	while (ok + 1 < ng) {
// 		int med = (ok + ng) / 2;
// 		if (hwABcomp(&arr[med], &x) > 0) {
// 			ok = med;
// 		} else {
// 			ng = med;
// 		}
// 	}
// 	return ok;
// }

int strAcomp(const struct_a *left, const struct_a *right){
	return ullcomp(&(left->a), &(right->a));
}

int strBcomp(const struct_b *left, const struct_b *right){
	return ullcomp(&(left->cost), &(right->cost));
}

int bitlet(char c){
	return (1 << (c - 'a'));
}

ull ulldiff(ull a, ull b){
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}


int fullfill(int x, int a, int b){
	int u = x / a;
	while (u >= 0) {
		if ((x - a * u) % b == 0) break;
		u--;
	}
	return u;
}

ull solve(){
	int i, j, ki;
	ull result = 0;

	qsort(a, n, sizeof(ull), ullcomp);

	for (i = 0; i < n; i++) {
		ull mustbe = ((n % 2) ? ((i + 1) / 2) * 2 : (i / 2) * 2 + 1);
		if (a[i] != mustbe) {
			puts("0");
			return 1;
		}
	}

	printf("%llu\n", bitpow(2, n / 2));

	return 0;
}
 
int main(void){
	int i, j;
	int x, y;

	scanf("%llu", &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%llu%llu%llu", &k, &va, &vb);
	for (i = 0; i < n; i++) {
		scanf("%llu", &a[i], &b[i]);
	}

	solve();

	// for (i = 0; i < m; i++) {
	// 	scanf("%llu%llu", &va, &vb);
	// 	solve();
	// }

	return 0;
}