Ujan has a lot of numbers in his boxes. He likes order and balance, so he decided to reorder the numbers.

There are $k$ boxes numbered from $1$ to $k$. The $i$-th box contains $n_i$ integer numbers. The integers can be negative. All of the integers are distinct. 

Ujan is lazy, so he will do the following reordering of the numbers exactly once. He will pick a single integer from each of the boxes, $k$ integers in total. Then he will insert the chosen numbers — one integer in each of the boxes, so that the number of integers in each box is the same as in the beginning. Note that he may also insert an integer he picked from a box back into the same box.

Ujan will be happy if the sum of the integers in each box is the same. Can he achieve this and make the boxes perfectly balanced, like all things should be?


-----Input-----

The first line contains a single integer $k$ ($1 \leq k \leq 15$), the number of boxes. 

The $i$-th of the next $k$ lines first contains a single integer $n_i$ ($1 \leq n_i \leq 5\,000$), the number of integers in box $i$. Then the same line contains $n_i$ integers $a_{i,1}, \ldots, a_{i,n_i}$ ($|a_{i,j}| \leq 10^9$), the integers in the $i$-th box. 

It is guaranteed that all $a_{i,j}$ are distinct.


-----Output-----

If Ujan cannot achieve his goal, output "No" in a single line. Otherwise in the first line output "Yes", and then output $k$ lines. The $i$-th of these lines should contain two integers $c_i$ and $p_i$. This means that Ujan should pick the integer $c_i$ from the $i$-th box and place it in the $p_i$-th box afterwards.

If there are multiple solutions, output any of those.

You can print each letter in any case (upper or lower).


-----Examples-----
Input
4
3 1 7 4
2 3 2
2 8 5
1 10

Output
Yes
7 2
2 3
5 1
10 4

Input
2
2 3 -2
2 -1 5

Output
No

Input
2
2 -10 10
2 0 -20

Output
Yes
-10 2
-20 1



-----Note-----

In the first sample, Ujan can put the number $7$ in the $2$nd box, the number $2$ in the $3$rd box, the number $5$ in the $1$st box and keep the number $10$ in the same $4$th box. Then the boxes will contain numbers $\{1,5,4\}$, $\{3, 7\}$, $\{8,2\}$ and $\{10\}$. The sum in each box then is equal to $10$.

In the second sample, it is not possible to pick and redistribute the numbers in the required way.

In the third sample, one can swap the numbers $-20$ and $-10$, making the sum in each box equal to $-10$.

Difficulty: VERY_HARD

Solutions:
def main():
	k = int(input())
	n = []
	a = []
	for i in range(k):
		line = [int(x) for x in input().split()]
		ni = line[0]
		ai = []
		n.append(ni)
		a.append(ai)
		for j in range(ni):
			ai.append(line[1 + j])
	(answer, c, p) = solve(k, n, a)
	if answer:
		print('Yes')
		for i in range(k):
			print(c[i], p[i] + 1)
	else:
		print('No')

def solve(k, n, a):
	(asum, sums) = calc_sums(k, n, a)
	if asum % k != 0:
		return (False, None, None)
	tsum = asum / k
	num_map = build_num_map(k, n, a)
	masks = [None] * (1 << k)
	answer = [False] * (1 << k)
	left = [0] * (1 << k)
	right = [0] * (1 << k)
	for i in range(k):
		for j in range(n[i]):
			(found, mask, path) = find_cycle(i, j, i, j, k, n, a, sums, tsum, num_map, 0, dict())
			if found:
				answer[mask] = True
				masks[mask] = path
	for mask_right in range(1 << k):
		if not masks[mask_right]:
			continue
		zeroes_count = 0
		for u in range(k):
			if 1 << u > mask_right:
				break
			if mask_right & 1 << u == 0:
				zeroes_count += 1
		for mask_mask in range(1 << zeroes_count):
			mask_left = 0
			c = 0
			for u in range(k):
				if 1 << u > mask_right:
					break
				if mask_right & 1 << u == 0:
					if mask_mask & 1 << c != 0:
						mask_left = mask_left | 1 << u
					c += 1
			joint_mask = mask_left | mask_right
			if answer[mask_left] and (not answer[joint_mask]):
				answer[joint_mask] = True
				left[joint_mask] = mask_left
				right[joint_mask] = mask_right
				if joint_mask == (1 << k) - 1:
					return build_answer(k, masks, left, right)
	if answer[(1 << k) - 1]:
		return build_answer(k, masks, left, right)
	return (False, None, None)

def build_answer(k, masks, left, right):
	c = [-1] * k
	p = [-1] * k
	pos = (1 << k) - 1
	while not masks[pos]:
		for (key, val) in masks[right[pos]].items():
			c[key] = val[0]
			p[key] = val[1]
		pos = left[pos]
	for (key, val) in masks[pos].items():
		c[key] = val[0]
		p[key] = val[1]
	return (True, c, p)

def build_num_map(k, n, a):
	result = dict()
	for i in range(k):
		for j in range(n[i]):
			result[a[i][j]] = (i, j)
	return result

def find_cycle(i_origin, j_origin, i, j, k, n, a, sums, tsum, num_map, mask, path):
	if mask & 1 << i != 0:
		if i == i_origin and j == j_origin:
			return (True, mask, path)
		else:
			return (False, None, None)
	mask = mask | 1 << i
	a_needed = tsum - (sums[i] - a[i][j])
	if a_needed not in num_map:
		return (False, None, None)
	(i_next, j_next) = num_map[a_needed]
	path[i_next] = (a[i_next][j_next], i)
	return find_cycle(i_origin, j_origin, i_next, j_next, k, n, a, sums, tsum, num_map, mask, path)

def calc_sums(k, n, a):
	sums = [0] * k
	for i in range(k):
		for j in range(n[i]):
			sums[i] = sums[i] + a[i][j]
	asum = 0
	for i in range(k):
		asum = asum + sums[i]
	return (asum, sums)
main()


def main():
	k = int(input())
	n = []
	a = []
	for i in range(k):
		line = [int(x) for x in input().split()]
		ni = line[0]
		ai = []
		n.append(ni)
		a.append(ai)
		for j in range(ni):
			ai.append(line[1 + j])
	(answer, c, p) = solve(k, n, a)
	if answer:
		print('Yes')
		for i in range(k):
			print(c[i], p[i] + 1)
	else:
		print('No')

def solve(k, n, a):
	(asum, sums) = calc_sums(k, n, a)
	if asum % k != 0:
		return (False, None, None)
	tsum = asum / k
	num_map = build_num_map(k, n, a)
	masks = [None] * (1 << k)
	simple = [False] * (1 << k)
	answer = [False] * (1 << k)
	left = [0] * (1 << k)
	right = [0] * (1 << k)
	by_last_one = [[] for _ in range(k)]
	for i in range(k):
		for j in range(n[i]):
			(found, mask, path) = find_cycle(i, j, i, j, k, n, a, sums, tsum, num_map, 0, [])
			if found and (not answer[mask]):
				answer[mask] = True
				masks[mask] = path
				simple[mask] = True
				by_last_one[calc_last_one(mask)].append(mask)
	if answer[(1 << k) - 1]:
		return build_answer(k, masks, left, right)
	for mask_right in range(2, 1 << k):
		if not simple[mask_right]:
			continue
		last_one = calc_last_one(mask_right)
		zeroes_count = 0
		alternative_sum = 0
		zero_list = []
		for u in range(last_one):
			if mask_right & 1 << u == 0:
				zeroes_count += 1
				alternative_sum += len(by_last_one[u])
				zero_list.append(u)
		if zeroes_count == 0:
			continue
		if alternative_sum < 1 << zeroes_count:
			for fill_last_zero in zero_list:
				for mask_left in by_last_one[fill_last_zero]:
					if mask_left & mask_right != 0:
						continue
					joint_mask = mask_left | mask_right
					if not answer[joint_mask]:
						answer[joint_mask] = True
						left[joint_mask] = mask_left
						right[joint_mask] = mask_right
						by_last_one[last_one].append(joint_mask)
						if joint_mask == (1 << k) - 1:
							return build_answer(k, masks, left, right)
		else:
			for mask_mask in range(1 << zeroes_count):
				mask_left = 0
				for u in range(zeroes_count):
					if mask_mask & 1 << u != 0:
						mask_left = mask_left | 1 << zero_list[u]
				joint_mask = mask_left | mask_right
				if answer[mask_left] and (not answer[joint_mask]):
					answer[joint_mask] = True
					left[joint_mask] = mask_left
					right[joint_mask] = mask_right
					by_last_one[last_one].append(joint_mask)
					if joint_mask == (1 << k) - 1:
						return build_answer(k, masks, left, right)
	return (False, None, None)

def calc_last_one(x):
	result = -1
	while x > 0:
		x = x >> 1
		result = result + 1
	return result

def build_answer(k, masks, left, right):
	c = [-1] * k
	p = [-1] * k
	pos = (1 << k) - 1
	while not masks[pos]:
		for (i, a, j) in masks[right[pos]]:
			c[i] = a
			p[i] = j
		pos = left[pos]
	for (i, a, j) in masks[pos]:
		c[i] = a
		p[i] = j
	return (True, c, p)

def build_num_map(k, n, a):
	result = dict()
	for i in range(k):
		for j in range(n[i]):
			result[a[i][j]] = (i, j)
	return result

def find_cycle(i_origin, j_origin, i, j, k, n, a, sums, tsum, num_map, mask, path):
	if mask & 1 << i != 0:
		if i == i_origin and j == j_origin:
			return (True, mask, path)
		else:
			return (False, None, None)
	mask = mask | 1 << i
	a_needed = tsum - (sums[i] - a[i][j])
	if a_needed not in num_map:
		return (False, None, None)
	(i_next, j_next) = num_map[a_needed]
	path.append((i_next, a[i_next][j_next], i))
	return find_cycle(i_origin, j_origin, i_next, j_next, k, n, a, sums, tsum, num_map, mask, path)

def calc_sums(k, n, a):
	sums = [0] * k
	for i in range(k):
		for j in range(n[i]):
			sums[i] = sums[i] + a[i][j]
	asum = 0
	for i in range(k):
		asum = asum + sums[i]
	return (asum, sums)

def __starting_point():
	main()
__starting_point()


from collections import defaultdict
data = defaultdict(list)
position = defaultdict()
nxt = defaultdict()
agg_sum = list()
k = int(input())
trace = defaultdict()
F = [False for x in range(1 << k)]
back = [0 for x in range(1 << k)]
total_sum = 0
res = [(0, 0) for x in range(k)]

def build_mask(trace_mask):
	if trace_mask == 0:
		return
	if trace.get(trace_mask):
		for data in trace.get(trace_mask):
			(fr, to, v) = data
			res[fr] = (v, to)
		return
	sub_mask = back[trace_mask]
	build_mask(sub_mask)
	build_mask(trace_mask - sub_mask)
for i in range(k):
	values = list(map(int, input().split(' ')))
	data[i] = values[1:]
	agg_sum.append(sum(data[i]))
	total_sum += agg_sum[i]
	for (cnt, v) in enumerate(data[i], 0):
		position[v] = (i, cnt)
if total_sum % k != 0:
	print('No')
	exit(0)
row_sum = total_sum // k
for i in range(k):
	for (cnt, value) in enumerate(data.get(i), 0):
		x = i
		y = cnt
		mask = 1 << x
		could = True
		circle = list()
		while True:
			next_value = row_sum - agg_sum[x] + data.get(x)[y]
			if position.get(next_value) is None:
				could = False
				break
			last_x = x
			last_y = y
			(x, y) = position.get(next_value)
			circle.append((x, last_x, next_value))
			if x == i and y == cnt:
				break
			if mask & 1 << x:
				could = False
				break
			mask |= 1 << x
		F[mask] |= could
		if could:
			trace[mask] = circle
for mask in range(1, 1 << k):
	sub = mask
	while sub > 0:
		if F[sub] and F[mask - sub]:
			F[mask] = True
			back[mask] = sub
			break
		sub = mask & sub - 1
if F[(1 << k) - 1]:
	print('Yes')
	build_mask((1 << k) - 1)
	for value in res:
		print(value[0], value[1] + 1)
else:
	print('No')


def main():
	k = int(input())
	n = []
	a = []
	for i in range(k):
		line = [int(x) for x in input().split()]
		ni = line[0]
		ai = []
		n.append(ni)
		a.append(ai)
		for j in range(ni):
			ai.append(line[1 + j])
	(answer, c, p) = solve(k, n, a)
	if answer:
		print('Yes')
		for i in range(k):
			print(c[i], p[i] + 1)
	else:
		print('No')

def solve(k, n, a):
	(asum, sums) = calc_sums(k, n, a)
	if asum % k != 0:
		return (False, None, None)
	tsum = asum / k
	num_map = build_num_map(k, n, a)
	masks = [None] * (1 << k)
	simple = [False] * (1 << k)
	for i in range(k):
		for j in range(n[i]):
			(found, mask, path) = find_cycle(i, j, i, j, k, n, a, sums, tsum, num_map, 0, dict())
			if found:
				simple[mask] = True
				masks[mask] = path
	for i in range(1 << k):
		if not simple[i]:
			continue
		mask = i
		zeroes_count = 0
		for u in range(k):
			if 1 << u > mask:
				break
			if mask & 1 << u == 0:
				zeroes_count += 1
		for mask_mask in range(1 << zeroes_count):
			mask_child = 0
			c = 0
			for u in range(k):
				if 1 << u > mask:
					break
				if mask & 1 << u == 0:
					if mask_mask & 1 << c != 0:
						mask_child = mask_child | 1 << u
					c += 1
			if masks[mask_child] and (not masks[mask_child | mask]):
				masks[mask_child | mask] = {**masks[mask_child], **masks[mask]}
				if mask_child | mask == (1 << k) - 1:
					c = [-1] * k
					p = [-1] * k
					d = masks[(1 << k) - 1]
					for (key, val) in d.items():
						c[key] = val[0]
						p[key] = val[1]
					return (True, c, p)
	if masks[(1 << k) - 1]:
		c = [-1] * k
		p = [-1] * k
		d = masks[(1 << k) - 1]
		for (key, val) in d.items():
			c[key] = val[0]
			p[key] = val[1]
		return (True, c, p)
	return (False, None, None)

def build_num_map(k, n, a):
	result = dict()
	for i in range(k):
		for j in range(n[i]):
			result[a[i][j]] = (i, j)
	return result

def find_cycle(i_origin, j_origin, i, j, k, n, a, sums, tsum, num_map, mask, path):
	if mask & 1 << i != 0:
		if i == i_origin and j == j_origin:
			return (True, mask, path)
		else:
			return (False, None, None)
	mask = mask | 1 << i
	a_needed = tsum - (sums[i] - a[i][j])
	if a_needed not in num_map:
		return (False, None, None)
	(i_next, j_next) = num_map[a_needed]
	path[i_next] = (a[i_next][j_next], i)
	return find_cycle(i_origin, j_origin, i_next, j_next, k, n, a, sums, tsum, num_map, mask, path)

def calc_sums(k, n, a):
	sums = [0] * k
	for i in range(k):
		for j in range(n[i]):
			sums[i] = sums[i] + a[i][j]
	asum = 0
	for i in range(k):
		asum = asum + sums[i]
	return (asum, sums)
main()