Hexadecimal likes drawing. She has drawn many graphs already, both directed and not. Recently she has started to work on a still-life «interesting graph and apples». An undirected graph is called interesting, if each of its vertices belongs to one cycle only — a funny ring — and does not belong to any other cycles. A funny ring is a cycle that goes through all the vertices just once. Moreover, loops are funny rings too.

She has already drawn the apples and some of the graph edges. But now it is not clear, how to connect the rest of the vertices to get an interesting graph as a result. The answer should contain the minimal amount of added edges. And furthermore, the answer should be the lexicographically smallest one. The set of edges (x1, y1), (x2, y2), ..., (xn, yn), where xi ≤ yi, is lexicographically smaller than the set (u1, v1), (u2, v2), ..., (un, vn), where ui ≤ vi, provided that the sequence of integers x1, y1, x2, y2, ..., xn, yn is lexicographically smaller than the sequence u1, v1, u2, v2, ..., un, vn. If you do not cope, Hexadecimal will eat you. ...eat you alive.

Input

The first line of the input data contains a pair of integers n and m (1 ≤ n ≤ 50, 0 ≤ m ≤ 2500) — the amount of vertices and edges respectively. The following lines contain pairs of numbers xi and yi (1 ≤ xi, yi ≤ n) — the vertices that are already connected by edges. The initial graph may contain multiple edges and loops.

Output

In the first line output «YES» or «NO»: if it is possible or not to construct an interesting graph. If the answer is «YES», in the second line output k — the amount of edges that should be added to the initial graph. Finally, output k lines: pairs of vertices xj and yj, between which edges should be drawn. The result may contain multiple edges and loops. k can be equal to zero.

Examples

Input

3 2
1 2
2 3


Output

YES
1
1 3
def dfs(v, graph):
	isloop = False
	lo, ro = graph

	# expand right
	pr, r = lo, ro
	expand_right = []
	while True:
		if len(v[r]) == 1:
			break
		else:
			nr1, nr2 = v[r]
			rn = nr1 if nr1 != pr else nr2
			expand_right.append(rn)
			if rn == lo: # we found loop
				isloop = True
				break
			pr = r
			r = rn

	if isloop:
		return True, graph + expand_right

	# expand left
	l, pl = lo, ro
	expand_left = []
	while True:
		if len(v[l]) == 1:
			break
		else:
			nl1, nl2 = v[l]
			nl = nl1 if nl1 != pl else nl2
			expand_left.append(nl)
			pl = l
			l = nl

	final_graph = expand_left[::-1] + graph + expand_right
	# if final_graph[0] > final_graph[-1]:
	# 	final_graph = final_graph[::-1]

	return False, final_graph

def findMinvalInLineEnds(lines):
	minval, minval_idx = 0xFFFF, None
	secval, secval_idx = 0xFFFF, None

	for i in range(len(lines)):
		if lines[i][0] < minval:
			secval = minval
			secval_idx = minval_idx
			minval = lines[i][0]
			minval_idx = i
		elif lines[i][0] < secval:
			secval = lines[i][0]
			secval_idx = i

	return minval, minval_idx, secval, secval_idx

def greedyConnect(lines, points):
	edges = []
	points.sort()

	if len(points) == 1 and len(lines) == 0:
		edges.append((points[0],points[0]))
		return edges

	while True:
		if len(lines) == 1 and len(points) == 0:
			edges.append((lines[0][0], lines[0][-1]))
			break

		minval_p = points[0] if len(points) > 0 else 0xFFFF
		secval_p = points[1] if len(points) > 1 else 0xFFFF
		minval_l, minval_idx_l, secval_l, secval_idx_l = findMinvalInLineEnds(lines)

		if minval_p < minval_l:
			if secval_p < minval_l: # connect 2 points to make a line
				edges.append((minval_p, secval_p))
				points = points[2:]
				lines.append([minval_p, secval_p])
			else: # connect point to the line
				edges.append((minval_p, minval_l))
				li = minval_idx_l
				lines[li] = [minval_p, lines[li][-1]]
				points = points[1:]
		else:
			# if minval is one end of line, we merge that line with a point or a line
			if minval_p < secval_l:
				edges.append((minval_l, minval_p))
				li = minval_idx_l
				lines[li][0] = minval_p
				if lines[li][0] > lines[li][-1]:
					lines[li] = [lines[li][-1], lines[li][0]]
				points = points[1:]
			else:
				edges.append((minval_l, secval_l))
				mil, sil = minval_idx_l, secval_idx_l
				lines[mil][0] = lines[sil][-1]
				if lines[mil][0] > lines[mil][-1]:
					lines[mil] = [lines[mil][-1], lines[mil][0]]
				del lines[sil]
	return edges

if __name__ == '__main__':
	n,m = tuple(map(int, input().split()))
	v = [[] for i in range(n)]

	for i in range(m):
		v1,v2 = tuple(map(int, input().split()))
		v1,v2 = v1-1,v2-1
		v[v1].append(v2)
		v[v2].append(v1)

	# validate input
	input_valid = True
	for i in range(n):
		if len(v[i]) > 2:
			input_valid = False
			break
		v[i].sort()

	if not input_valid:
		print('NO')
		exit()

	loops = []
	lines = []
	points = []

	visited = [False for i in range(n)]

	for i in range(n):
		if visited[i]:
			continue
		elif len(v[i]) == 0:
			points.append(i)
			visited[i] = True
		elif len(v[i]) == 1 and v[i] == i:
			loops.append([i,i])
			visited[i] = True
		else:
			isloop, graph = dfs(v,[i,v[i][0]])
			for gi in graph:
				visited[gi] = True
			if isloop:
				loops.append(graph)
			else:
				lines.append(graph)

	if len(loops) > 0:
		if len(loops) == 1 and len(points) == 0 and len(lines) == 0:
			print('YES')
			print(0)
			exit()
		else:
			print('NO')
			exit()

	# print('loops')
	# for p in loops:
	# 	print('\t{}'.format([e+1 for e in p]))
	# print('lines')
	# for p in lines:
	# 	print('\t{}'.format([e+1 for e in p]))
	# print('points')
	# for p in points:
	# 	print('\t{}'.format(p+1))

	# We only need two ends of the line
	for li in range(len(lines)):
		e1,e2 = lines[li][0], lines[li][-1]
		lines[li] = [e1,e2] if e1<e2 else [e2,e1]

	edges = greedyConnect(lines, points)

	print('YES')
	print(len(edges))
	for v1,v2 in edges:
		v1 += 1
		v2 += 1
		if v1 < v2:
			print('{} {}'.format(v1,v2))
		else:
			print('{} {}'.format(v2,v1))