Problem:
Score : 900 points

Problem Statement

Takahashi has an ability to generate a tree using a permutation (p_1,p_2,...,p_n) of (1,2,...,n), in the following process:

First, prepare Vertex 1, Vertex 2, ..., Vertex N.
For each i=1,2,...,n, perform the following operation:

If p_i = 1, do nothing.

If p_i \neq 1, let j' be the largest j such that p_j < p_i. Span an edge between Vertex i and Vertex j'.

Takahashi is trying to make his favorite tree with this ability.
His favorite tree has n vertices from Vertex 1 through Vertex n, and its i-th edge connects Vertex v_i and w_i.
Determine if he can make a tree isomorphic to his favorite tree by using a proper permutation.
If he can do so, find the lexicographically smallest such permutation.

Notes

For the definition of isomorphism of trees, see wikipedia. Intuitively, two trees are isomorphic when they are the "same" if we disregard the indices of their vertices.

Constraints

2 \leq n \leq 10^5

1 \leq v_i, w_i \leq n

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

n
v_1 w_1
v_2 w_2
:
v_{n-1} w_{n-1}

Output

If there is no permutation that can generate a tree isomorphic to Takahashi's favorite tree, print -1.
If it exists, print the lexicographically smallest such permutation, with spaces in between.

Sample Input 1

6
1 2
1 3
1 4
1 5
5 6

Sample Output 1

1 2 4 5 3 6

If the permutation (1, 2, 4, 5, 3, 6) is used to generate a tree, it looks as follows:

This is isomorphic to the given graph.

Sample Input 2

6
1 2
2 3
3 4
1 5
5 6

Sample Output 2

1 2 3 4 5 6

Sample Input 3

15
1 2
1 3
2 4
2 5
3 6
3 7
4 8
4 9
5 10
5 11
6 12
6 13
7 14
7 15

Sample Output 3

-1

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

#if 0
cat <<EOF >mistaken-paste
#endif
// thanks for @rsk0315_h4x

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

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007
#define VERYBIG 2000000000000007LL

#define MOD 1000000007
#define FOD  998244353
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1000000

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <functional>
#include <array>

using std::queue;
using std::priority_queue;
using std::stack;
using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
using std::get;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

typedef struct {
	int32_t a;
	int32_t b;
} hw;

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

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

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

ull n, m;
ull h, w;
ull k;
ull q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

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 modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

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

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(ull);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}

bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

sll a[N_MAX + 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX + 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
ull c[N_MAX + 5];
ull d[N_MAX + 5];
sll e[N_MAX];
char s[N_MAX + 1];
// char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
// char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
sll table[3005][3005];
// here we go

ull deg[N_MAX];
ull acdeg[N_MAX];
sll next[N_MAX][2];
ull p[N_MAX], l = 0;

void make (ull a[], ull d[]) {
	sll i, j, ki;

	i = 0;
	ull curr = 0;
	for (j = 0; j < l; j++) {
		for (ki = 0; ki < d[j]; ki++) {
			a[i] = curr + 1 + ki;
			i++;
		}
		a[i] = curr;
		i++;

		curr += d[j] + 1;
	}
}

ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	ull *dpcell;

	if (n == 2) {
		puts("1 2");
		return 0;
	}
	if (n == 3) {
		puts("1 2 3");
		return 0;
	}

	for (i = 0; i < n - 1; i++) {
		deg[a[i]]++;
		deg[b[i]]++;
	}
	for (i = 0; i < n; i++) {
		if (deg[i] > 1) {
			l++;
		}
	}
	for (i = 0; i < n - 1; i++) {
		if (deg[a[i]] > 1 && deg[b[i]] > 1) {
			acdeg[a[i]]++;
			acdeg[b[i]]++;
		}
	}
	for (i = 0; i < n; i++) {
		if (acdeg[i] == 1) {
			p[0] = i;
			break;
		}
	}
	if (l == 1) {
		// 1 3 4 5 ... n-1 2 n
		printf("1 ");
		for (i = 3; i <= n - 1; i++) {
			printf("%lld ", i);
		}
		printf("2 %lld\n", n);
		return 0;
	}
	for (i = p[0] + 1; i < n; i++) {
		if (acdeg[i] == 1) {
			p[l - 1] = i;
			break;
		}
	}
	if (i == n) goto fail;
	for (i = 0; i < n; i++) {
		if (deg[i] == 1 || i == p[0] || i == p[l - 1]) continue;
		if (acdeg[i] != 2) goto fail;
	}
	for (i = 0; i < n; i++) {
		next[i][0] = -1;
	}
	for (i = 0; i < n - 1; i++) {
		if (deg[a[i]] > 1 && deg[b[i]] > 1) {
			next[a[i]][(next[a[i]][0] < 0) ? 0 : 1] = b[i];
			next[b[i]][(next[b[i]][0] < 0) ? 0 : 1] = a[i];
		}
	}
	// for (i = 0; i < n; i++) printf("%lld - %lld\n", next[i][0], next[i][1]);
	// 	printf("%lld ~~ %lld\n", p[0], p[l - 1]);
	for (i = 1; i < l - 1; i++) {
		p[i] = ((i == 1) ? 0 : p[i - 2]) ^ next[p[i - 1]][0] ^ next[p[i - 1]][1];
		// printf("%lld\n", p[i]);
	}
	// puts("!");
	// fflush(stdout);
	for (i = 0; i < l; i++) {
		d[i] = deg[p[i]] - 2;
	}
	for (i = l - 1; i >= 0; i--) {
		d[i + 1] = d[i];
	}
	l += 2;
	d[0] = d[l - 1] = 0;

	make(a, d);
	i = 0;
	j = l - 1;
	while (i < j) {
		d[i] ^= d[j];
		d[j] ^= d[i];
		d[i] ^= d[j];
		i++;
		j--;
	}
	make(b, d);

	bool isa = true;
	for (i = 0; i < n; i++) {
		if (a[i] < b[i]) {
			isa = true;
			break;
		}
		if (a[i] > b[i]) {
			isa = false;
			break;
		}
	}
	for (i = 0; i < n; i++) {
		printf("%llu%c", (isa ? a : b)[i] + 1, (i == n - 1 ? '\n' : ' '));
	}

	// printf("%lld\n", result);
	// printf("%.15lf\n", dresult);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("Yay!");
	return 0;

	fail:
	// puts("NO");
	// puts("No");
	// puts("0");
	puts("-1");
	// puts("-1 -1 -1");
	// puts("Impossible");
	return 1;
}

int32_t main (void) {
	int32_t i, j;
	int32_t x, y;



	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu%llu", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// scanf("%llu%llu%llu", &ua, &ub, &uc, &ud);
	// scanf("%s", t);
	// scanf("%lld", &m);
	for (i = 0; i < n - 1; i++) {
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
		scanf("%lld", &a[i]);
		scanf("%lld", &b[i]);
		// scanf("%lld", &c[i]);
		// scanf("%lld", &d[i]);
		a[i]--;
		b[i]--;
		// c[i]--;
		// d[i]--;
		// xy[i].a--;
		// xy[i].b--;
		// tup[i].a--;
		// tup[i].b--;
	}
	// scanf("%llu", &m, &k);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// for (i = 0; i < n * 2; i++) {
	// 	scanf("%lld", &b[i]);
	// 	// b[i]--;
	// 	// c[i]--;
	// }
	// scanf("%llu", &q);

	// for (i = 0; i < q; i++) {
	// 	scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	xy[i].a--;
	// 	xy[i].b--;
	// }

	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	// for (i = 0; i < h; i++) {
	// 	scanf("%s", s[i]);
	// }
	// scanf("%llu", &q);

	solve();

	return 0;
}